{"id":250628,"date":"2022-09-30T09:18:05","date_gmt":"2022-09-30T07:18:05","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=250628"},"modified":"2025-01-08T21:56:47","modified_gmt":"2025-01-08T20:56:47","slug":"identite-remarquable","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/identite-remarquable\/","title":{"rendered":"Tout savoir sur les identit\u00e9s remarquables &#8211; 3\u1d49 \ud83d\ude0e"},"content":{"rendered":"\n<p>Le <a href=\"https:\/\/sherpas.com\/blog\/programme-maths-3eme\/\">programme de math\u00e9matiques de 3\u1d49<\/a> est riche en<strong> complexit\u00e9<\/strong>. C\u2019est pourquoi chez les Sherpas, on s\u2019engage \u00e0 te donner <strong>quelques explications suppl\u00e9mentaires<\/strong> sur tes cours. Aujourd\u2019hui, on va te parler des <strong>identit\u00e9s remarquables<\/strong>, chapitre incontournable de ton ann\u00e9e de troisi\u00e8me ! Pr\u00eat ? Allons-y ! \ud83d\udd25<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Identit\u00e9 remarquable, le pourquoi du comment \ud83e\uddd0<\/h2>\n\n\n\n<p>Avant de se lancer dans des explications et des d\u00e9monstrations qui donnent mal \u00e0 la t\u00eate, voyons les bases de cette le\u00e7on.&nbsp;<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 \u00c9tymologie<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Le mot <\/span><b>identit\u00e9<\/b><span style=\"font-weight: 400\"> vient du latin <\/span><i><span style=\"font-weight: 400\">identitas<\/span><\/i><span style=\"font-weight: 400\"> qui signifie \u201c<\/span><b>le m\u00eame<\/b><span style=\"font-weight: 400\">\u201d. Le terme <\/span><b>identit\u00e9<\/b><span style=\"font-weight: 400\"> d\u00e9finit la <\/span><b>similitude entre deux choses<\/b><span style=\"font-weight: 400\"> (ou plus). En maths, une identit\u00e9 repr\u00e9sente une \u00e9galit\u00e9 entre deux \u00e9l\u00e9ments (m\u00eame s\u2019ils n\u2019ont pas la m\u00eame valeur). Cette \u00e9galit\u00e9 se justifie et est v\u00e9rifi\u00e9e \u00e0 l\u2019aide de calcul.\u00a0\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Le mot <\/span><b>remarquable<\/b><span style=\"font-weight: 400\"> est un d\u00e9riv\u00e9 du mot <\/span><i><span style=\"font-weight: 400\">remarquer <\/span><\/i><span style=\"font-weight: 400\">qui signifie \u201c<\/span><b>qui attire l\u2019attention<\/b><span style=\"font-weight: 400\">\u201d. Autrement dit, <\/span><b>remarquable<\/b><span style=\"font-weight: 400\"> donne \u00e0 son objet <\/span><b>quelque chose de particulier<\/b><span style=\"font-weight: 400\">, qui ne passe pas inaper\u00e7u.\u00a0<\/span><\/li>\n<\/ul>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Une<strong> identit\u00e9 remarquable <\/strong>est une <strong>expression math\u00e9matique<\/strong> unique. Elle sert \u00e0 \u00e9tablir une formule simple et efficace pour <strong>calculer deux \u00e9galit\u00e9s<\/strong>. Si par exemple deux nombres, deux aires, deux <a href=\"https:\/\/sherpas.com\/blog\/calculer-un-perimetre\/\">p\u00e9rim\u00e8tres<\/a> ou encore deux poids sont \u00e9gaux.&nbsp;<\/p>\n\n\n\n<p>Elle permet d\u2019acc\u00e9l\u00e9rer des calculs, simplifier certaines \u00e9critures, factoriser ou m\u00eame d\u00e9velopper des expressions math\u00e9matiques. Notamment,<strong> r\u00e9soudre des \u00e9quations du second degr\u00e9<\/strong> (x<sup>2<\/sup>).<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p><span style=\"font-weight: 400\">\ud83d\udca1 Anecdote<\/span><\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Les <\/span><b>premi\u00e8res traces d\u2019identit\u00e9 remarquable au second degr\u00e9<\/b><span style=\"font-weight: 400\"> voient le jour \u00e0 l\u2019\u00e9poque des Babyloniens. D\u00e9j\u00e0, ils utilisaient cette technique pour calculer des superficies \u00e0 l\u2019aide de la g\u00e9om\u00e9trie !<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>Exemple :&nbsp;<\/p>\n\n\n\n<p>Voici une surface g\u00e9om\u00e9trique \u2014 ici un carr\u00e9 \u2014, pour t\u2019expliquer l\u2019origine de ce calcul. Tu peux observer que ce carr\u00e9 est compos\u00e9 de 4 parties. Il existe deux mani\u00e8res de la calculer.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"350\" height=\"353\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/09\/identite-remarquable.png\" alt=\"identit\u00e9 remarquable\" class=\"wp-image-250631\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/09\/identite-remarquable.png?q=90&amp;org_if_sml=1&amp;w=350 350w, https:\/\/adymrxvmro.cloudimg.io\/v7\/https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/09\/identite-remarquable.png?q=90&amp;org_if_sml=1&amp;w=270 270w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>\ud83d\udc49 On utilise la version simple : c\u00f4t\u00e9\u00d7c\u00f4t\u00e9 = aire du carr\u00e9. La longueur d\u2019un c\u00f4t\u00e9 est \u00e9gale \u00e0 a+b. Ce qui nous donne (a+b)\u00d7(a+b)= (a+b)\u00b2<\/p>\n\n\n\n<p>\ud83d\udc49 On calcul partie par partie.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ce que l\u2019on d\u00e9finit comme <em>a\u00b2<\/em>, n\u2019est autre que la multiplication de la valeur <em>a<\/em> par elle-m\u00eame : a\u00b2 = a\u00d7a. Autrement dit, <em>a\u00b2<\/em> peut \u00eatre consid\u00e9r\u00e9 comme l\u2019aire d\u2019un carr\u00e9 dont le c\u00f4t\u00e9 mesure <em>a<\/em> (base de la le\u00e7on sur les aires vu en 6\u1d49).<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Il en va de m\u00eame pour <em>b\u00b2 :<\/em> c\u2019est un carr\u00e9 de longueur <em>b<\/em>, donc sa surface est \u00e9gale \u00e0 b\u00d7b = b\u00b2.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>En ce qui concerne les deux autres parties, elles sont \u00e9gales \u00e0 a\u00d7b = ab, il y en a deux ainsi le pour faire plus simple, on l\u2019\u00e9crit : 2ab soit 2\u00d7a\u00d7b.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>C\u2019est ainsi qu\u2019on d\u00e9couvre l\u2019identit\u00e9 remarquable car <strong>(a+b)\u00b2<\/strong> = <strong>a\u00b2 + 2ab + b\u00b2<\/strong>&nbsp;<\/p>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p>Rappel : <a href=\"https:\/\/sherpas.com\/blog\/comment-calculer-une-aire\/\">Comment calculer une aire ?<\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<p>Il existe beaucoup d\u2019identit\u00e9s remarquables. En 3\u1d49, tu \u00e9tudie <strong>celle du second degr\u00e9<\/strong>, qui sont au nombre de<strong> trois<\/strong> :<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>\ud83d\udc49&nbsp; (a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2&nbsp;<\/p>\n\n\n\n<p>\ud83d\udc49&nbsp; (a-b)\u00b2 = a\u00b2 \u2013 2ab + b\u00b2<\/p>\n\n\n\n<p>\ud83d\udc49&nbsp; (a+b) (a-b) = a\u00b2 \u2013 b\u00b2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/Hwa1ZXSpqJbQBHIUcS\/giphy.gif\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>\ud83d\udccd <em>a<\/em> et <em>b<\/em> d\u00e9signent des nombres (entier, rationnel ou r\u00e9el).&nbsp;<\/p>\n\n\n\n<p>\ud83d\udccd Un chiffre au carr\u00e9 repr\u00e9sente la multiplication du chiffre par lui-m\u00eame.&nbsp;<\/p>\n\n\n\n<p>Exemples : 2<sup>2<\/sup> = 2\u00d72 = 4<\/p>\n\n\n\n<p>Chacune d\u2019entre elles repr\u00e9sente le <strong>calcul litt\u00e9ral d\u2019une \u00e9quation<\/strong>. Tu l\u2019as s\u00fbrement d\u00e9j\u00e0 vu pendant tes cours de maths de 4\u1d49, mais ici aussi, il faut utiliser <strong>le principe de distributivit\u00e9<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Pour obtenir la somme de ton \u00e9quation, tu auras besoin de faire soit un d\u00e9veloppement avec le principe de la distributivit\u00e9, soit une <a href=\"https:\/\/sherpas.com\/blog\/factorisation\/\">factorisation<\/a>.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p><span style=\"font-weight: 400\">\ud83d\udcd6 D\u00e9finition<\/span><\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Un <\/span><b>d\u00e9veloppement<\/b><span style=\"font-weight: 400\"> est l\u2019action de transformer un produit (multiplication) en somme (addition ou soustraction).<\/span><\/p>\n<p><span style=\"font-weight: 400\">Une <\/span><b>factorisation<\/b><span style=\"font-weight: 400\"> est mat\u00e9rialis\u00e9e par la transformation d\u2019une somme en produit. <\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p><a href=\"https:\/\/sherpas.com\/blog\/comment-etre-fort-en-maths\/\">Comment \u00eatre fort en maths ?<\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zdWJqZWN0PU1hdGhzJnNpZ251cD10cnVl\" data-banner=\"2\" data-name=\"CPM1 Maths\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Louise2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Louise<\/p>                          <p class=\"push__teachers-school\">Mines ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Fabien2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fabien<\/p>                          <p class=\"push__teachers-school\">T\u00e9l\u00e9com Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Bastien2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Bastien<\/p>                          <p class=\"push__teachers-school\">Polytechnique<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Pierre2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Pierre<\/p>                          <p class=\"push__teachers-school\">ESSEC<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">16\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Simon2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Simon<\/p>                          <p class=\"push__teachers-school\">4e ann\u00e9e de m\u00e9decine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Jade2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Jade<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Besoin d&#8217;un <span style=\"color: #4cc583;\">prof particulier<\/span> de maths ? <span role=\"image\" aria-label=\"\u2728\">\u2728<\/span><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos Sherpas sont l\u00e0 pour t&#8217;aider \u00e0 progresser et prendre confiance en toi !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        JE PRENDS UN COURS GRATUIT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">La premi\u00e8re identit\u00e9 remarquable \u2728<\/h2>\n\n\n\n<p>L\u2019\u00e9galit\u00e9 <strong>(a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2<\/strong>&nbsp; est la premi\u00e8re que l\u2019on retrouve dans <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Livre_II_des_%C3%89l%C3%A9ments_d%27Euclide#:~:text=Le%20livre%20II%20des%20%C3%89l%C3%A9ments,%2C%20en%20particulier%20al%2DKhwarizmi.\" target=\"_blank\" rel=\"noreferrer noopener\">le livre II des \u00c9l\u00e9ments d\u2019Euclide<\/a>.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\ud83d\udcd7 <\/strong>D\u00e9monstration<strong>&nbsp;<\/strong><\/h3>\n\n\n\n<p>Pour d\u00e9montrer une \u00e9galit\u00e9, il suffit de la d\u00e9velopper. Voici la m\u00e9thode pour d\u00e9velopper ton \u00e9galit\u00e9.&nbsp;<br>Si <em>a<\/em> et <em>b<\/em> sont deux nombres, alors on peut d\u00e9velopper (a+b)<sup>2<\/sup>.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>(a+b)<sup>2&nbsp; <\/sup>= (a+b) x (a+b)&nbsp;<\/p>\n\n\n\n<p>= a\u00d7a + a\u00d7b + b\u00d7a + b\u00d7b&nbsp;<\/p>\n\n\n\n<p>= a<sup>2<\/sup> + ab + ba + b<sup>2<\/sup><\/p>\n\n\n\n<p>= a<sup>2<\/sup> + 2ab + b<sup>2<\/sup><br>Donc,<strong> <\/strong>(a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/QVn2VCvGFQnjP6ILf1\/giphy.gif\" alt=\"\" style=\"width:240px;height:240px\"\/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Exemples&nbsp;<\/h3>\n\n\n\n<p>\ud83d\udc49 Sans inconnue.<\/p>\n\n\n\n<p>Si <em>a<\/em> = 5 et <em>b<\/em> = 2.<\/p>\n\n\n\n<p>On a : (5+2)<sup>2<\/sup><\/p>\n\n\n\n<p>(5+2)<sup>2 <\/sup>&nbsp;= (5+2) x (5+2)<\/p>\n\n\n\n<p>= 5\u00d75 + 2\u00d75 + 5\u00d72 + 2\u00d72<\/p>\n\n\n\n<p>= 5<sup>2<\/sup> + 10 + 10 + 2<sup>2<\/sup><\/p>\n\n\n\n<p>= 25 + 10 + 10 + 4&nbsp;<\/p>\n\n\n\n<p>= 49&nbsp;<\/p>\n\n\n\n<p>Maintenant, tu comprends la d\u00e9monstration sur le plan technique. Il faut tout de m\u00eame savoir qu\u2019une identit\u00e9 remarquable est, en grande majorit\u00e9 du temps, rencontr\u00e9e avec une inconnue. \ud83e\udd13<\/p>\n\n\n\n<p>\ud83d\udc49 Avec une inconnue.&nbsp;<\/p>\n\n\n\n<p>Si <em>a<\/em> = 4x et <em>b<\/em> = 2.<\/p>\n\n\n\n<p>On a : (4x+2)<sup>2<\/sup><\/p>\n\n\n\n<p>(4x+2)<sup>2<\/sup>= (4x+2) x (4x+2)&nbsp;<\/p>\n\n\n\n<p>=(4x)<sup>2<\/sup> + 4x \u00d7 2 + 2 \u00d7 4x + 2<sup>2<\/sup><\/p>\n\n\n\n<p><sup><\/sup>= 16x\u00b2 + 8x + 8x + 4&nbsp;<\/p>\n\n\n\n<p>= 16x\u00b2 + 16x + 4&nbsp;<\/p>\n\n\n\n<p>\u274c Attention : Lorsqu\u2019il y a une inconnue, ne pas oublier de mettre le nombre avec x\u00b2 &#8211; <em>(6x)\u00b2 &#8211;<\/em> entre parenth\u00e8ses pour ne pas fausser les r\u00e9sultats !<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u2712\ufe0f <\/strong>Exercices<strong>&nbsp;<\/strong><\/h3>\n\n\n\n<p>D\u00e9veloppe les expressions suivantes :<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(x+6)\u00b2&nbsp;<\/li>\n\n\n\n<li>(5+2x)\u00b2<\/li>\n\n\n\n<li>(x+10)\u00b2<\/li>\n\n\n\n<li>(6x+1)\u00b2<\/li>\n<\/ol>\n\n\n\n<p>R\u00e9ponses&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(x+6)\u00b2 = x\u00b2 + 6x + 6x + 6\u00b2&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= x\u00b2 + 12x + 36<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(5+2x)\u00b2 = 5\u00b2 + 5x \u00d7 2 + 2 \u00d7 5x + 2\u00b2&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 25 + 10x + 10x + 4<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 25 + 20x + 4<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(x+10)\u00b2 = x\u00b2 + 10x + 10x + 10\u00b2<\/li>\n<\/ul>\n\n\n\n<p>= x\u00b2 + 20x + 100<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(6x+1)\u00b2 = (6x)\u00b2 + 6x \u00d7 1 + 1 \u00d7 6x + 1\u00b2<\/li>\n<\/ul>\n\n\n\n<p>= 36x\u00b2 + 12x + 1<\/p>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p><a href=\"https:\/\/sherpas.com\/blog\/vaincre-la-peur-des-maths\/\">Vaincre sa peur des maths ?<\/span><\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zdWJqZWN0PU1hdGhzJnNpZ251cD10cnVl\" data-banner=\"2\" data-name=\"CPM2 Maths\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Bastien2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Bastien<\/p>                          <p class=\"push__teachers-school\">Polytechnique<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Fabien2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fabien<\/p>                          <p class=\"push__teachers-school\">T\u00e9l\u00e9com Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Emilie2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Emilie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Lyon<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Agathe2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Agathe<\/p>                          <p class=\"push__teachers-school\">ENS Lyon<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/David2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">David<\/p>                          <p class=\"push__teachers-school\">EDHEC<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">25\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Sophie2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Sophie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Bordeaux<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">12\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Martin2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Martin<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">23\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Ton premier <span style=\"color: #4cc483;\">cours particulier<\/span> de maths est <span style=\"color: #4cc483;\">offert<\/span> ! <span role=\"image\" aria-label=\"\ud83c\udf81\">\ud83c\udf81<\/span><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Tous nos profs sont pass\u00e9s par les meilleures \u00e9coles de France !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        J\u2019EN PROFITE !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">La deuxi\u00e8me identit\u00e9 remarquable \ud83d\udcab<\/h2>\n\n\n\n<p>La seconde identit\u00e9 remarquable est un d\u00e9riv\u00e9 de la premi\u00e8re. La seule diff\u00e9rence, c&#8217;est le signe utilis\u00e9 :&nbsp; <strong>(a-b)\u00b2 = a\u00b2 \u2013 2ab + b\u00b2<\/strong>&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 D\u00e9monstration<strong>&nbsp;<\/strong><\/h3>\n\n\n\n<p>Comme vu pr\u00e9c\u00e9demment, pour utiliser cette identit\u00e9 remarquable, il faut la d\u00e9velopper. C\u2019est parti !&nbsp;<\/p>\n\n\n\n<p>Si <em>a<\/em> et <em>b<\/em> sont deux nombres, alors on peut d\u00e9velopper (a-b)<sup>2<\/sup>.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>(a-b)\u00b2 &nbsp; = (a-b) x (a-b)<\/p>\n\n\n\n<p>= axa &#8211; a\u00d7b &#8211; b\u00d7a &#8211; b\u00d7(-b)&nbsp;<\/p>\n\n\n\n<p>= a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/T4yi6e5UF4vXx57VOJ\/giphy.gif\" alt=\"\" style=\"width:360px;height:203px\"\/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>\u274c Attention : En math\u00e9matiques, un chiffre n\u00e9gatif multipli\u00e9 par ce m\u00eame chiffre n\u00e9gatif devient positif. On te propose une phrase mn\u00e9motechnique : moins par moins \u00e9gale plus (- x &#8211; = +).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exemples&nbsp;<\/h3>\n\n\n\n<p>\ud83d\udc49 Sans inconnue.<\/p>\n\n\n\n<p>Si <em>a<\/em> = 5 et <em>b<\/em> = 2.<\/p>\n\n\n\n<p>On a : (5-2)<sup>2<\/sup><\/p>\n\n\n\n<p>(5-2)<sup>2 <\/sup>&nbsp;= (5-2) x (5-2)<\/p>\n\n\n\n<p>= 5\u00d75 &#8211; 2\u00d75 &#8211; 5\u00d72<strong> &#8211; 2\u00d7 (-2)<\/strong>&nbsp;&nbsp;<\/p>\n\n\n\n<p>= 5\u00d75 &#8211; 2\u00d75 &#8211; 5\u00d72 <strong>+ 2\u00b2<\/strong><\/p>\n\n\n\n<p>= 5<sup>2<\/sup> &#8211; 10 &#8211; 10 + 2<sup>2<\/sup><\/p>\n\n\n\n<p>= 25 &#8211; 10 &#8211; 10 + 4&nbsp;<\/p>\n\n\n\n<p>= 9<\/p>\n\n\n\n<p>D\u00e9sormais, tu peux voir que chaque identit\u00e9 remarquable est propre \u00e0 elle-m\u00eame. Encore une fois, il est rare que tu la rencontres sans inconnue.&nbsp;<\/p>\n\n\n\n<p>\ud83d\udc49 Avec une inconnue.&nbsp;<\/p>\n\n\n\n<p>Si <em>a<\/em> = 4x et <em>b<\/em> = 2.<\/p>\n\n\n\n<p>On a : (4x-2)<sup>2<\/sup><\/p>\n\n\n\n<p>(4x-2)<sup>2<\/sup>= (4x-2) x (4x-2)&nbsp;<\/p>\n\n\n\n<p>=(4x)<sup>2<\/sup> &#8211; 4x \u00d7 2 &#8211; 2 \u00d7 4x <strong>&#8211; 2 x (-2)<\/strong><\/p>\n\n\n\n<p><strong><\/strong>=<strong> <\/strong>(4x)<sup>2<\/sup> &#8211; 4x \u00d7 2 &#8211; 2 \u00d7 4x <strong>+ 2\u00b2<\/strong><\/p>\n\n\n\n<p><sup><\/sup>= 16x\u00b2 &#8211; 8x &#8211; 8x + 4&nbsp;<\/p>\n\n\n\n<p>= 16x\u00b2 &#8211; 16x + 4&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2712\ufe0f Exercices<\/h3>\n\n\n\n<p>D\u00e9veloppe les expressions suivantes :&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(6x-1)\u00b2&nbsp;<\/li>\n\n\n\n<li>(8-5x)\u00b2<\/li>\n\n\n\n<li>(2x-4)\u00b2<\/li>\n\n\n\n<li>(10x-5)\u00b2<\/li>\n<\/ol>\n\n\n\n<p>R\u00e9sultats&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(6x-1)\u00b2 = (6x)\u00b2 &#8211; 6x \u00d7 1 &#8211; 1 \u00d7 6x <strong>+<\/strong> 1\u00b2<\/li>\n<\/ul>\n\n\n\n<p>= 36x\u00b2 &#8211; 6x &#8211; 6x + 1<\/p>\n\n\n\n<p>= 36x\u00b2 &#8211; 12x + 1<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(8-5x)\u00b2 = 8\u00b2 &#8211; 8 \u00d7 5x &#8211; 5x \u00d7 8 + (5x)\u00b2<\/li>\n<\/ul>\n\n\n\n<p>= 64 &#8211; 40x &#8211; 40x + 25x\u00b2<\/p>\n\n\n\n<p>= 64 &#8211; 80x + 25x\u00b2<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(2x-4)\u00b2 = (2x)\u00b2 &#8211; 2x \u00d7 4 &#8211; 4 \u00d7 2x + 4\u00b2&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>= 4x\u00b2 &#8211; 8x &#8211; 8x + 16<\/p>\n\n\n\n<p>= 4x\u00b2 &#8211; 16x + 16&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(10x-5)\u00b2 = (10x)\u00b2 &#8211; 10x\u00d75 &#8211; 5\u00d710x + 5\u00b2&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>= 100x\u00b2 &#8211; 50x &#8211; 50x + 25&nbsp;<\/p>\n\n\n\n<p>= 100x\u00b2 &#8211; 100x + 25<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zdWJqZWN0PVByJUMzJUE5cGFyYXRpb24rYnJldmV0JnNpZ251cD10cnVl\" data-banner=\"2\" data-name=\"CPE1 brevet\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Thibault2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Thibault<\/p>                          <p class=\"push__teachers-school\">ENS Paris Ulm<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Agathe2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Agathe<\/p>                          <p class=\"push__teachers-school\">ENS Lyon<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Louise2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Louise<\/p>                          <p class=\"push__teachers-school\">Mines ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Noemie2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">No\u00e9mie<\/p>                          <p class=\"push__teachers-school\">M2 en droit \u00e0 Assas<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Victor2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Victor<\/p>                          <p class=\"push__teachers-school\">ESCP<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">25\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Sophie2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Sophie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Bordeaux<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">12\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Antoine2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Antoine<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">18\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Tu veux <span style=\"color: #000000;\">cartonner au brevet<\/span> ? \u2728<\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos profs sont l\u00e0 pour t\u2019aider \u00e0 progresser !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        JE PRENDS UN COURS GRATUIT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">La troisi\u00e8me identit\u00e9 remarquable \ud83c\udf1f<\/h2>\n\n\n\n<p>Jamais deux sans trois comme on dit, voici enfin la troisi\u00e8me identit\u00e9 remarquable : <strong>(a+b) (a-b) = a\u00b2 \u2013 b\u00b2&nbsp;<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd9 D\u00e9monstration<strong>&nbsp;<\/strong><\/h3>\n\n\n\n<p>Si <em>a<\/em> et <em>b<\/em> sont deux nombres, alors on peut d\u00e9velopper (a+b) (a-b).<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>(a+b) (a-b) = a\u00d7a &#8211; a\u00d7b + b\u00d7a &#8211; b\u00d7b<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; = a\u00b2 <strong>&#8211; ab + ab<\/strong> &#8211; b\u00b2<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=&nbsp; a\u00b2 &#8211; b\u00b2<\/p>\n\n\n\n<p>Donc : <strong>&nbsp;<\/strong>(a+b) (a-b) = a\u00b2 \u2013 b\u00b2&nbsp;<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/WZytyZa0C0OVvzMS0V\/giphy.gif\" alt=\"\" style=\"width:360px;height:288px\"\/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>\u274c Attention : En math\u00e9matiques, un nombre n\u00e9gatif additionn\u00e9 \u00e0 ce m\u00eame nombre positif s\u2019annule : il est \u00e9gal \u00e0 0. On te propose un deuxi\u00e8me mn\u00e9motechnique : plus par moins (ou moins par plus) est \u00e9gal \u00e0 z\u00e9ro (+ par &#8211; = 0).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exemples&nbsp;<\/h3>\n\n\n\n<p>\ud83d\udc49 Sans inconnue.<\/p>\n\n\n\n<p>Si <em>a<\/em> = 3 et <em>b<\/em> = 2.<\/p>\n\n\n\n<p>(3+2) (3-2) = 3\u00b2 &#8211; 3\u00d72 + 2\u00d73 &#8211; 2\u00b2<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; = 9 <strong>&#8211; 6 + 6<\/strong> &#8211; 4<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; = 9 &#8211; 4&nbsp;<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; = 5<\/p>\n\n\n\n<p><strong><em>&#8211; 6 + 6 = 0&nbsp;<\/em><\/strong><\/p>\n\n\n\n<p>\u00c0 pr\u00e9sent que tu visualises bien cet ultime calcul, sache que, comme pour les deux pr\u00e9c\u00e9dents, tu le rencontreras toujours avec une inconnue.<\/p>\n\n\n\n<p>\ud83d\udc49 Avec une inconnue.<\/p>\n\n\n\n<p>Si <em>a<\/em> = 6x et <em>b<\/em> = 4.<\/p>\n\n\n\n<p>(6x+4) (6x-4) = (6x)\u00b2 &#8211; 4\u00b2&nbsp;<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 36x\u00b2 &#8211; 16<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2712\ufe0f Exercices<strong>&nbsp;&nbsp;<\/strong><\/h3>\n\n\n\n<p>D\u00e9veloppe les expressions suivantes :<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(4x-2) (4x+2)&nbsp;<\/li>\n\n\n\n<li>(x+8) (x-8)<\/li>\n\n\n\n<li>(10x+3) (10x-3)<\/li>\n\n\n\n<li>(6x-7) (6x+7)<\/li>\n<\/ol>\n\n\n\n<p>R\u00e9ponses<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(4x-2) (4x+2) = (4x)\u00b2 &#8211; (-2)\u00b2<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 16x\u00b2 &#8211; 4&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(x+8) (x-8) = x\u00b2 \u2013 8\u00b2<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; = x\u00b2 \u2013 64<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(10x+3) (10x-3) = (10x)\u00b2 \u2013 3\u00b2<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; = 100x\u00b2 \u2013 9&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(6x-7) (6x+7) = (6x)\u00b2 \u2013 (-7)\u00b2<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 36x\u00b2 \u2013 49<\/p>\n\n\n\n<p>Si tu as des difficult\u00e9s \u00e0 comprendre cette le\u00e7on, on a une autre solution pour toi ! Tu peux faire appelle \u00e0 un de <a href=\"https:\/\/sherpas.com\/cours\/maths\">nos super professeurs particuliers de maths<\/a>. Tu peux choisir le prof id\u00e9al pour toi en recherchant selon ton niveau, la mati\u00e8re que tu souhaites am\u00e9liorer et ta zone g\u00e9ographique. N\u2019h\u00e9site pas \u00e0 faire un tour sur notre plateforme. \ud83e\udd17<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">La pratique \ud83e\uddd1\u200d\ud83d\udcbb<\/h2>\n\n\n\n<p>Maintenant, tu connais les trois identit\u00e9s remarquables. Tu sais comment les utiliser et les d\u00e9velopper. La seule chose qu\u2019il te reste \u00e0 apprendre est de les reconna\u00eetre pour savoir laquelle utiliser.&nbsp;<\/p>\n\n\n\n<p>Pour \u00e7a aussi, chez les Sherpas, on a une m\u00e9thode infaillible \u00e0 te donner (mais c\u2019est un secret alors ne le dis \u00e0 personne) !&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Reconna\u00eetre l\u2019identit\u00e9 remarquable \ud83d\udc40<\/h3>\n\n\n\n<p>Pour reconna\u00eetre l\u2019identit\u00e9 remarquable que tu dois utiliser dans ton \u00e9nonc\u00e9, rien de plus simple ! On te donne la petite astuce <em>(mais ne le r\u00e9p\u00e8te pas)<\/em>.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>La premi\u00e8re identit\u00e9 est <strong>une addition :<\/strong>&nbsp; (a<strong>+<\/strong>b)\u00b2&nbsp;<\/p>\n\n\n\n<p>La deuxi\u00e8me identit\u00e9 est <strong>une soustraction :<\/strong> (a<strong>&#8211;<\/strong>b)\u00b2<\/p>\n\n\n\n<p>La troisi\u00e8me est <strong>les deux en m\u00eame temps :<\/strong> (a<strong>+<\/strong>b) (a<strong>&#8211;<\/strong>b)&nbsp;<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/Iy8KblbfM53N8E4JaJ\/giphy-downsized-large.gif\" alt=\"\" style=\"width:240px;height:240px\"\/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>Tadam ! Les identit\u00e9s remarquables n\u2019ont d\u00e9sormais plus aucun secret pour toi. N\u2019oublie pas de bien t\u2019entrainer. On ne le r\u00e9p\u00e9tera jamais assez : faire des exercices est le meilleur moyen de r\u00e9ussir tes examens ! \ud83e\udd73<\/p>\n\n\n\n<p>Si tu souhaites anticiper les cours de math\u00e9matiques qui t\u2019attendent l\u2019an prochain, tu peux jeter un \u0153il au <a href=\"https:\/\/sherpas.com\/blog\/programme-maths-seconde\/\">programme de maths de Seconde\u202f<\/a>!<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;250628&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;42&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;4.1&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Tu as aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;4.1\\\/5 - (42 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Tout savoir sur les identit\u00e9s remarquables - 3\u1d49 \ud83d\ude0e&quot;,&quot;width&quot;:&quot;116.4&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 116.4px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            4.1\/5 - (42 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Le programme de math\u00e9matiques de 3\u1d49 est riche en complexit\u00e9. C\u2019est pourquoi chez les Sherpas, on s\u2019engage \u00e0 (&#8230;)<\/p>\n","protected":false},"author":326,"featured_media":250653,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":true,"footnotes":""},"category":[803,810],"tag":[77,770,352],"class_list":["post-250628","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-college","tag-fiche-revision","tag-troisieme"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/250628","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/326"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=250628"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/250628\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/250653"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=250628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=250628"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=250628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}