{"id":265182,"date":"2026-10-26T10:42:51","date_gmt":"2026-10-26T09:42:51","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=265182"},"modified":"2026-10-26T10:45:51","modified_gmt":"2026-10-26T09:45:51","slug":"calculs-litteraux","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/calculs-litteraux\/","title":{"rendered":"Calcul litt\u00e9ral : un monde sans chiffres \ud83d\ude2f !"},"content":{"rendered":"\n<p>Toi qui pensais que les math\u00e9matiques n\u2019\u00e9taient que des calculs avec des chiffres et des nombres, d\u00e9sol\u00e9 de te dire que ce n\u2019est pas exactement le cas. Bienvenue dans le calcul litt\u00e9ral, c\u2019est-\u00e0-dire le calcul avec des lettres, qui prend de plus en plus de place au coll\u00e8ge jusqu\u2019en 3e.&nbsp;<\/p>\n\n\n\n<p>On va voir aujourd\u2019hui que <strong>les lettres se tapent l\u2019incruste dans tes <a href=\"https:\/\/sherpas.com\/cours\/maths\">cours de maths<\/a><\/strong>. Et oui, tu les utilises pour <a href=\"https:\/\/sherpas.com\/blog\/comment-faire-une-bonne-dissertation\/\">\u00e9crire ta meilleure r\u00e9daction de fran\u00e7ais<\/a> d\u2019habitude, mais l\u00e0, elles vont se retrouver dans tes \u00e9quations. C\u2019\u00e9tait d\u00e9j\u00e0 bien assez compliqu\u00e9 avec des nombres, tu me diras \ud83d\ude21.&nbsp;<\/p>\n\n\n\n<p>Allez, ne te d\u00e9courage pas ! Dans cet article, tu vas voir \u00e0 quoi sert le calcul litt\u00e9ral et comment r\u00e9duire, d\u00e9velopper et factoriser une expression, avec un exemple corrig\u00e9 pour chaque r\u00e8gle. Prends ta calculatrice et suis les Sherpas l\u00e0 o\u00f9 une lettre peut se compter.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"cest-quoi-le-calcul-litteral\">C\u2019est quoi le calcul litt\u00e9ral ? \ud83d\udd22\ud83d\udd20<\/h2>\n\n\n\n<p>Le calcul litt\u00e9ral, c\u2019est le calcul avec des lettres. Une lettre (souvent x, a ou n) d\u00e9signe un nombre qu\u2019on ne conna\u00eet pas encore, ou bien n\u2019importe quel nombre. On lui applique les m\u00eames r\u00e8gles qu\u2019aux nombres pour r\u00e9duire, d\u00e9velopper ou factoriser une expression litt\u00e9rale, et pour r\u00e9soudre une \u00e9quation. <\/p>\n\n\n\n<p>Le monde des math\u00e9matiques est vaste et complexe et pour cela, il a fallu que l\u2019homme invente les chiffres, puis qu\u2019il se dise que, finalement, ajouter une lettre dans un calcul et bah ce n\u2019est pas si mal que \u00e7a. Et voil\u00e0 comment sont n\u00e9s l\u2019expression litt\u00e9rale et le calcul litt\u00e9ral.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"definitions-et-origine\">D\u00e9finitions et origine \u2712\ufe0f<\/h3>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 D\u00e9finition<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Une expression litt\u00e9rale est <\/span><b>une expression math\u00e9matique contenant une ou plusieurs lettres qui d\u00e9signent des nombres<\/b><span style=\"font-weight: 400\">.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">Le \u00ab calcul litt\u00e9ral \u00bb signifie \u00ab calcul avec des lettres \u00bb. Cela englobe de nombreuses \u00e9quations et in\u00e9quations.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p><strong>L&rsquo;alg\u00e8bre a fait des progr\u00e8s prodigieux <\/strong>gr\u00e2ce aux math\u00e9maticiens fran\u00e7ais Fran\u00e7ois Vi\u00e8te (1540-1603) et Albert Girard (1595-1632) \ud83e\uddd1\u200d\ud83d\udd2c.<\/p>\n\n\n\n<p>Au lieu d&rsquo;exprimer les solutions \u00e0 des probl\u00e8mes math\u00e9matiques en langage courant, ils utilis\u00e8rent dans un premier temps des chiffres. Jusque-l\u00e0, \u00e7a ne semble pas si fou. Mais leur plus brillante id\u00e9e a \u00e9t\u00e9 <strong>d&rsquo;utiliser des lettres pour d\u00e9signer des valeurs donn\u00e9es et des inconnues \ud83d\udc4f<\/strong>.<\/p>\n\n\n\n<p>Ainsi, un \u00e9nonc\u00e9 tel que : \u00ab Trouver un nombre dont le triple ajout\u00e9 au nombre quatre vaut z\u00e9ro \u00bb est devenu : \u00ab R\u00e9soudre 3x + 4 = 0 \u00bb. Un probl\u00e8me qui n\u00e9cessitait jadis plusieurs pages se r\u00e9sout d\u00e9sormais en quelques lignes de calcul.<\/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>Si tu penses qu\u2019elles ne servent pas \u00e0 grand-chose, voici <a href=\"https:\/\/sherpas.com\/blog\/utiliser-maths-vie-courante\/\">9 fa\u00e7ons d\u2019utiliser les maths dans la vie courante !<\/a> \ud83d\udc46<\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"le-penseur-du-calcul-litteral\">Le penseur du calcul litt\u00e9ral \ud83d\udd0d<\/h3>\n\n\n\n<p>C\u2019est entre 1571 et 1591 que Fran\u00e7ois Vi\u00e8te (1540-1603) publie deux ouvrages, l\u2019un sur la trigonom\u00e9trie et l\u2019autre sur l\u2019alg\u00e8bre (<em>Canon mathematicus<\/em> et <em>In artem analyticem isagoge<\/em>), qui repr\u00e9sentent un grand pas en avant pour l\u2019alg\u00e8bre. Pour Vi\u00e8te, <strong>le calcul litt\u00e9ral a pour but clair de r\u00e9soudre tous les probl\u00e8mes<\/strong>. Les inconnues sont donc d\u00e9sign\u00e9es par des voyelles et les grandeurs connues par des consonnes \ud83d\udd21.&nbsp;<\/p>\n\n\n\n<p>Sacr\u00e9 Fran\u00e7ois ! Allez, voyons comment les calculs litt\u00e9raux fonctionnent maintenant.&nbsp;<\/p>\n\n\n<section class=\"relance\">\n        <div >\n                            <a rel=\"nofollow\" target=\"_blank\" href=\"https:\/\/sherpas.com\/funnel-student-qualification?subject=Maths\">\n                    <div class=\"relance__container\"\n                        >\n                        \n                                                        <picture>\n                            <source srcset=\"https:\/\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-4.jpg\" media=\"(min-width: 999px)\">\n                            <source srcset=\"https:\/\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-4.jpg\" media=\"(max-width: 999px)\">\n                                <img decoding=\"async\"\n                                    src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-4.jpg\"\n                                    alt=\"Personne qui donne des cours particuliers\"\n                                >\n                            <\/picture>\n                                                <div class=\"relance__content\">\n                            \n                                <div class=\"relance__title\"> <p>Tu gal\u00e8res en maths ? Trouve ton prof particulier chez les Sherpas !<\/p>\n<\/div>\n                                                        <button type=\"button\"\n                                    class=\"relance__button btn btn-white\">\n                                Trouve ton prof de maths !\n                            <\/button>\n                        <\/div>\n                    <\/div>\n                <\/a>\n                    <\/div>\n    <\/section>\n\n    \n\n\n<h2 class=\"wp-block-heading\" id=\"calcul-litteral-les-regles-et-la-formule-de-base\">Calcul litt\u00e9ral : les r\u00e8gles et la formule de base \u2604\ufe0f<\/h2>\n\n\n\n<p>La formule de base du calcul litt\u00e9ral, c\u2019est la distributivit\u00e9 : k(a + b) = ka + kb et k(a \u2212 b) = ka \u2212 kb. Lue de gauche \u00e0 droite, elle sert \u00e0 d\u00e9velopper ; lue de droite \u00e0 gauche, elle sert \u00e0 factoriser. Deux r\u00e8gles d\u2019\u00e9criture sont \u00e0 retenir : 3x signifie 3 \u00d7 x et x\u00b2 signifie x \u00d7 x.<\/p>\n\n\n\n<p>Ne sois pas effray\u00e9, on va t\u2019expliquer au mieux pour que tu ressortes de cet article en ayant tout compris !<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"la-distributivite\">&nbsp;La distributivit\u00e9 \ud83d\udc49 <\/h3>\n\n\n\n<p>On va d\u00e9tailler un peu plus cette formule : k \u00d7 (a + b) = k \u00d7 a + k \u00d7 b ; soit k(a + b) = ka + kb. C\u2019est le m\u00eame principe pour la soustraction : k \u00d7 (a &#8211; b) = k \u00d7 a \u2212 k \u00d7 b ; soit k(a &#8211; b) = ka &#8211; kb.<\/p>\n\n\n\n<p>C\u2019est bon, tu commences \u00e0 saisir ?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/rKxEIq5DnszGsWHGZn\/giphy.gif\" alt=\"Personnage de dessin anim\u00e9 qui est perdu\"\/><\/figure>\n<\/div>\n\n\n<p>C\u2019est ce qu\u2019on nomme la \u00ab distributivit\u00e9 \u00bb, car <strong>en d\u00e9veloppant l\u2019expression, on \u00ab distribue \u00bb le facteur k sur chaque terme de la parenth\u00e8se<\/strong>.<\/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>Si tu es f\u00e2ch\u00e9 avec les multiplications, on t\u2019invite \u00e0 <a href=\"https:\/\/sherpas.com\/blog\/apprendre-les-tables-de-multiplication-par-coeur\/\">apprendre tes tables comme par magie \ud83e\uddd9!\u00a0<\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"le-developpement\">Le d\u00e9veloppement \ud83d\ude42<\/h4>\n\n\n\n<p>D\u00e9velopper signifie que l&rsquo;on <strong>transforme une multiplication en une somme ou en une diff\u00e9rence<\/strong>.<\/p>\n\n\n\n<p>Dans les formules pr\u00e9c\u00e9dentes, on a transform\u00e9 le produit de k par (a + b) (ou (a \u2212b)) en une somme (ou une diff\u00e9rence). Donc : k \u00d7 (a + b) et k \u00d7 (a \u2212 b), sont devenus : ka + kb et ka &#8211; kb.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1Exemple<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">D\u00e9velopper l\u2019expression 3(4x &#8211; 6).<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">D\u2019apr\u00e8s les formules de distributivit\u00e9, on a : 3(4x &#8211; 6) = 3 \u00d7 4x &#8211; 3 \u00d7 6 = 12x &#8211; 18.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"la-factorisation\">La factorisation \ud83e\udd0f<\/h4>\n\n\n\n<p>En revanche, <strong>factoriser signifie faire le chemin inverse : une somme ou une diff\u00e9rence devient un produit<\/strong>. Si on reprend l\u2019exemple de tout \u00e0 l\u2019heure, mais que l&rsquo;on factorise au lieu de d\u00e9velopper, on peut passer de \u00ab\u00a0k \u00d7 a + k \u00d7 b ou k \u00d7 a &#8211; k \u00d7 b\u00a0\u00bb aux formes factoris\u00e9es que sont  \u00ab\u00a0k(a+b) et k(a-b)\u00a0\u00bb.<\/p>\n\n\n\n<p>La <a href=\"https:\/\/sherpas.com\/blog\/factorisation\/\">factorisation<\/a>, comme tu peux le voir, transforme une somme en produit : elle consiste <strong>\u00e0 rep\u00e9rer un facteur commun \u00e0 tous les termes (ici k, commun \u00e0 ka et \u00e0 kb)<\/strong> et \u00e0 le mettre devant les parenth\u00e8ses.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 Exemples<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Factorisons par x l\u2019expression 5x + 8x.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><span style=\"font-weight: 400\">5x + 8x = x(5 + 8) = 13x.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">On va ajouter quelques lettres et on va maintenant r\u00e9duire l\u2019expression 4a + 3b \u2212 8a + 6b, en regroupant les termes en a puis les termes en b. <\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><span style=\"font-weight: 400\">4a + 3b &#8211; 8a + 6b = 4a &#8211; 8a + 3b + 6b = a(4 &#8211; 8) + b(3 + 6) = &#8211; 4a + 9b.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"la-double-distributivite-%e2%80%bc\">La double distributivit\u00e9 \u203c\ufe0f<\/h3>\n\n\n\n<p>La double distributivit\u00e9 porte bien son nom et signifie qu\u2019il faut juste que <strong>tu distribues deux fois et pas une \ud83d\udc4d<\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/3oFzlUThksB7Atw3L2\/giphy.gif\" alt=\"Personne qui te fait comprendre que c'est logique\"\/><figcaption class=\"wp-element-caption\">Logique !<\/figcaption><\/figure>\n<\/div>\n\n\n<p>On s\u2019en sert pour les expressions du style :&nbsp;(a + b) (c + d) tel que a, b, c et d sont des <a href=\"https:\/\/sherpas.com\/blog\/nombre-relatif\/\" data-type=\"post\" data-id=\"254000\">nombres relatifs<\/a> (positifs ou n\u00e9gatifs, entiers ou non). On distribue donc \u00ab a \u00bb sur \u00ab c \u00bb et \u00ab d \u00bb ; et \u00ab b \u00bb sur \u00ab c \u00bb et \u00ab d \u00bb. Autrement dit, on fait la multiplication de \u00ab a \u00bb par \u00ab c \u00bb puis par \u00ab d \u00bb et ensuite de \u00ab b \u00bb par \u00ab c \u00bb puis  par \u00ab d \u00bb.&nbsp;<\/p>\n\n\n\n<p>Ce qui nous am\u00e8ne \u00e0 : <strong>(a + b) (c + d) = ac + ad + bc + bd<\/strong>.<br>D\u2019ailleurs, c&rsquo;est pareil avec la soustraction : (a + b) (c &#8211; d) = a x c + a x (-d) + b x c + b x (-d) = ac &#8211; ad + bc &#8211; bd.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udea8\u00a0 Petit rappel sur les nombres n\u00e9gatifs<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Regarde bien ce d\u00e9veloppement !\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">(a \u2013 b) (c \u2013 d)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">= a x c + a x (-d) + (-b) x c + (-b) x (-d)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">= ac + (-ad) + (-bc) + bd\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">= ac \u2013 ad \u2013 bc + bd.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">En effet, lorsque tu multiplies un nombre positif par un nombre n\u00e9gatif, le r\u00e9sultat est n\u00e9gatif. Ex : 3 \u00d7 (\u22124) = \u221212.\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">Mais, <\/span><b>lorsque tu multiplies deux nombres n\u00e9gatifs entre eux, cette fois, le r\u00e9sultat est positif<\/b><span style=\"font-weight: 400\">. Ex : (-3) x (-7) = 21.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Tu sais d\u00e9sormais ce qu\u2019est la distributivit\u00e9, ce qui est la base des calculs litt\u00e9raux, mais corsons un peu les choses !<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"la-triple-distributivite\">La triple distributivit\u00e9 \u2716\ufe0f<\/h3>\n\n\n\n<p>La triple distributivit\u00e9 sert \u00e0 d\u00e9velopper un produit de trois facteurs, comme (a + b)(c + d)(e + f). La m\u00e9thode tient en deux \u00e9tapes : tu d\u00e9veloppes d\u2019abord deux facteurs avec la double distributivit\u00e9, puis tu multiplies chaque terme obtenu par le troisi\u00e8me facteur. Avant de r\u00e9duire, tu dois trouver 2 \u00d7 2 \u00d7 2 = 8 produits.<\/p>\n\n\n\n<p>Exemple : d\u00e9veloppons (x + 1)(x + 2)(x + 3). \u00c9tape 1 : (x + 1)(x + 2) = x\u00b2 + 2x + x + 2 = x\u00b2 + 3x + 2. \u00c9tape 2 : (x\u00b2 + 3x + 2)(x + 3) = x\u00b3 + 3x\u00b2 + 3x\u00b2 + 9x + 2x + 6 = x\u00b3 + 6x\u00b2 + 11x + 6. Pour v\u00e9rifier, remplace x par 1 : (1 + 1)(1 + 2)(1 + 3) = 2 \u00d7 3 \u00d7 4 = 24 et 1 + 6 + 11 + 6 = 24, les deux valeurs sont bien \u00e9gales.<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9mdW5uZWwtc3R1ZGVudC1xdWFsaWZpY2F0aW9u\" 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 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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 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\/Olivier2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Olivier<\/p>                          <p class=\"push__teachers-school\">La Sorbonne<\/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\">23\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\/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\">29\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\">29\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\" id=\"a-quoi-sert-le-calcul-litteral\">&nbsp;\u00c0 quoi sert le calcul litt\u00e9ral ? \ud83d\ude80<\/h2>\n\n\n\n<p>Le calcul litt\u00e9ral sert \u00e0 \u00e9crire une r\u00e8gle valable pour tous les nombres, \u00e0 prouver qu\u2019une propri\u00e9t\u00e9 est toujours vraie et \u00e0 r\u00e9soudre des probl\u00e8mes gr\u00e2ce aux \u00e9quations. Il permet aussi de traduire un programme de calcul en expression, puis d\u2019aborder les fonctions. C\u2019est l\u2019outil qui fait passer de l\u2019arithm\u00e9tique \u00e0 l\u2019alg\u00e8bre. <\/p>\n\n\n\n<p>Exemple : si tu additionnes trois entiers qui se suivent, tu obtiens forc\u00e9ment un multiple de 3. Prouvons-le. En notant n le premier, on obtient n + (n + 1) + (n + 2) = 3n + 3 = 3(n + 1), qui s\u2019\u00e9crit bien 3 \u00d7 un entier.<\/p>\n\n\n\n<p>Apr\u00e8s avoir vu les bases, on va aller un peu plus loin et voir comment les lettres peuvent \u00eatre utilis\u00e9es dans tes cours de math\u00e9matiques.<\/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>Apprends diff\u00e9remment et regarde notre article sur <a href=\"https:\/\/sherpas.com\/blog\/film-maths\/\">7 films qui vont te faire aimer les maths \ud83c\udfa5 !\u00a0<\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"lexpression-litterale\">L\u2019expression litt\u00e9rale \ud83d\udd8b\ufe0f<\/h3>\n\n\n\n<p>Une expression litt\u00e9rale peut s\u2019apparenter \u00e0 : A = 5a + 6b \u2013 4 par exemple.<\/p>\n\n\n\n<p>Pour calculer la valeur d\u2019une expression litt\u00e9rale, on remplace chaque lettre par le nombre donn\u00e9, puis on applique les priorit\u00e9s de calcul. Avec a = 2 et b = 3, on obtient A = 5 \u00d7 2 + 6 \u00d7 3 \u2212 4 = 10 + 18 \u2212 4 = 24.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 Pour info<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Une lettre est aussi appel\u00e9e \u00ab variable \u00bb dans une expression litt\u00e9rale.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Pour t\u2019y retrouver, prends l\u2019habitude de <strong>mettre en ordre une expression<\/strong>. Changer l\u2019ordre des termes d\u2019une somme ne modifie pas sa valeur, mais l\u2019expression devient plus lisible.<\/p>\n\n\n\n<p>Pour cela, <strong>il faut ordonner de fa\u00e7on d\u00e9croissante les exposants des variables<\/strong>.<\/p>\n\n\n\n<p>Voici l\u2019expression litt\u00e9rale B = 15 + 7x\u00b2 \u2013 3x + x\u00b3 &nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>Pour rendre cette expression plus lisible, on l\u2019\u00e9crit sous cette forme : B = x\u00b3 + 7x\u00b2 \u2013 3x + 15. \u2705<\/p>\n\n\n\n<p>D\u2019ailleurs, dans une expression litt\u00e9rale o\u00f9 le signe \u00ab &#8211; \u00bb est plac\u00e9 devant des parenth\u00e8ses<strong>, il faut changer les signes des termes \u00e0 l\u2019int\u00e9rieur de ces parenth\u00e8ses<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Ex : B = (3x\u00b2 + 5x\u00b2 + x\u00b2) &#8211; (7x + 2x &#8211; 6)&nbsp;<\/p>\n\n\n\n<p>B = 3x\u00b2 + 5x\u00b2 + x\u00b2 &#8211; 7x &#8211; 2x + 6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>B = 9x\u00b2 &#8211; 9x + 6<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"les-identites-remarquables\">Les identit\u00e9s remarquables \ud83d\udc40<\/h3>\n\n\n\n<p>Elles permettent d\u2019acc\u00e9l\u00e9rer des calculs, notamment<strong> pour r\u00e9soudre des \u00e9quations du second degr\u00e9<\/strong>\u00a0(x<sup>2<\/sup>). En bref, tu dois simplement les <a href=\"https:\/\/sherpas.com\/blog\/comment-apprendre-par-coeur-rapidement\/\">apprendre par c\u0153ur<\/a> : les <a href=\"https:\/\/sherpas.com\/blog\/identite-remarquable\/\">3 identit\u00e9s remarquables<\/a> que l\u2019on va voir te permettront par la suite de d\u00e9velopper ou factoriser en un seul coup. Finis les longs calculs !<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/chzz1FQgqhytWRWbp3\/giphy.gif\" alt=\"Les mignons qui sont tous content\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\" id=\"carre-dune-difference\">Carr\u00e9 d\u2019une diff\u00e9rence \u2796<\/h4>\n\n\n\n<p>(a-b)\u00b2 = (a-b) (a-b) = a\u00b2 \u2013 ab &#8211; ba + b\u00b2<\/p>\n\n\n\n<p>Donc <strong>(a-b)\u00b2 = a\u00b2 \u2013 2ab + b\u00b2<\/strong><\/p>\n\n\n\n<p>Le carr\u00e9 d\u2019une somme \u2795&nbsp;<\/p>\n\n\n\n<p>(a+b)\u00b2 = (a+b) (a+b) = a\u00b2 + ab + ba + b\u00b2<\/p>\n\n\n\n<p>Ce qui nous donne : <strong>(a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"produit-de-la-somme-par-la-difference\">Produit de la somme par la diff\u00e9rence \u2795\u2796<\/h4>\n\n\n\n<p>(a+b)(a-b) = a x a + a x (-b) + b x a + b x (-b) = a\u00b2 \u2013 ab + ab \u2013 b\u00b2<\/p>\n\n\n\n<p>Donc <strong>(a+b)(a-b) = a\u00b2 \u2013 b\u00b2<\/strong><\/p>\n\n\n\n<p>Ces trois identit\u00e9s remarquables se lisent dans les deux sens. Pour d\u00e9velopper : (x + 3)\u00b2 = x\u00b2 + 2 \u00d7 x \u00d7 3 + 3\u00b2 = x\u00b2 + 6x + 9. Pour factoriser une diff\u00e9rence de deux carr\u00e9s : x\u00b2 \u2212 25 = x\u00b2 \u2212 5\u00b2 = (x + 5)(x \u2212 5).<\/p>\n\n\n\n<p>Et voil\u00e0 retiens ces trois r\u00e9sultats et tu feras des merveilles dans ton cours. D\u2019ailleurs si tu souhaites t\u2019am\u00e9liorer, n\u2019h\u00e9site pas \u00e0 prendre <a href=\"https:\/\/sherpas.com\/cours\/maths\/online\">des cours particuliers de maths en ligne<\/a> avec l\u2019un de nos Sherpas !&nbsp;<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9mdW5uZWwtc3R1ZGVudC1xdWFsaWZpY2F0aW9u\" data-banner=\"2\" data-name=\"Cours part\u2019 global #1 = CPG1\" 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\/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                                              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                       <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">29\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\/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\">29\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\/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\">28\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\/Margot2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Margot<\/p>                          <p class=\"push__teachers-school\">Arts et M\u00e9tiers 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                                         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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">22\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\/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                        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           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                                            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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">27\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>Ton premier cours particulier est offert ! <span role=\"img\" aria-label=\"\ud83c\udf81\">\ud83c\udf81<\/span><!-- notionvc: 91b6b7d7-50f2-46f4-ae1f-ecbabe834aad --><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos profs sont pass\u00e9s par les meilleures \u00e9coles et universit\u00e9s.<!-- notionvc: 21bb66b6-b36d-4ce8-8950-173722d75a1e --><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: #ffffff; border-color: ; background-color: \"\n\n                                    >\n                                        J&rsquo;EN PROFITE MAINTENANT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"les-equations\">&nbsp;Les \u00e9quations \ud83d\udff0<\/h3>\n\n\n\n<p>Finissons par un mot qui en effraie beaucoup, surtout au coll\u00e8ge : <a href=\"https:\/\/sherpas.com\/blog\/equation-inequation\/\">les \u00e9quations<\/a> \ud83d\ude31 !&nbsp;<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 D\u00e9finition<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><b>Une \u00e9quation lie des inconnues \u00e0 des valeurs connues<\/b><span style=\"font-weight: 400\">. Et pour le point historique, l\u2019\u00e9tude des \u00e9quations (connue, aujourd&rsquo;hui, sous le nom \u00ab alg\u00e8bre \u00bb) a nettement progress\u00e9 gr\u00e2ce aux recherches des math\u00e9maticiens arabo-persans \ud83c\udf0d.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"les-equations-du-premier-degre\">Les \u00e9quations du premier degr\u00e9 \u2668\ufe0f<\/h4>\n\n\n\n<p>Ce sont <strong>les \u00e9quations qui s\u2019\u00e9crivent sous la forme \u00ab ax + b = cx + d \u00bb<\/strong> o\u00f9 a, b, c et d sont des nombres tels que a \u2260 c (a est diff\u00e9rent de c). D\u2019ailleurs, une \u00e9quation du premier degr\u00e9 a une unique solution.<\/p>\n\n\n\n<p>Passons \u00e0 un exemple, afin que tu comprennes au mieux. Essayons de r\u00e9soudre 6x &#8211; 7 = 4x + 3.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\u21aa\ufe0f Info<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Pour r\u00e9soudre une \u00e9quation du premier degr\u00e9, on rassemble les termes en x dans un membre de l\u2019\u00e9galit\u00e9, et les nombres seuls dans l\u2019autre membre.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b>Pour faire passer un terme de l\u2019autre c\u00f4t\u00e9 du signe \u00e9gal, il faut changer son signe<\/b><span style=\"font-weight: 400\"> (on fait la m\u00eame op\u00e9ration sur les deux membres). <\/span><b>\u26d4<\/b><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Dans notre cas, on met \u00ab 4x \u00bb \u00e0 gauche et cela donne :<\/p>\n\n\n\n<p>Premi\u00e8rement, 6x &#8211; 7 &#8211; 4x = 3<\/p>\n\n\n\n<p>Deuxi\u00e8mement, on fait passer le \u00ab -7 \u00bb \u00e0 droite, ce qui nous am\u00e8ne \u00e0 :&nbsp;<\/p>\n\n\n\n<p>6x &#8211; 4x = 3 + 7<\/p>\n\n\n\n<p>Troisi\u00e8mement, on calcule chaque c\u00f4t\u00e9 :&nbsp;<\/p>\n\n\n\n<p>2x = 10<\/p>\n\n\n\n<p>Et pour finir, on divise par deux chaque c\u00f4t\u00e9 de l\u2019\u00e9quation pour arriver \u00e0 une solution o\u00f9 X est \u00e9gal \u00e0 un nombre, ce qui nous donne :&nbsp;<\/p>\n\n\n\n<p>2x\/2 = 10\/2<\/p>\n\n\n\n<p><strong>X = 5<\/strong><\/p>\n\n\n\n<p>On peut m\u00eame v\u00e9rifier notre r\u00e9ponse en reprenant le probl\u00e8me de d\u00e9part :&nbsp;<\/p>\n\n\n\n<p>6 x 5 &#8211; 7 = 4 x 5 + 3<\/p>\n\n\n\n<p>30 &#8211; 7 = 20 + 3<\/p>\n\n\n\n<p>23 = 23<\/p>\n\n\n\n<p>Ce qui est juste ! F\u00e9licitations \u00e0 tous \ud83c\udf89 !<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/6nuiJjOOQBBn2\/giphy.gif\" alt=\"Barney Stinson qui applaudit\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\" id=\"les-equations-du-second-degre\">Les \u00e9quations du second degr\u00e9 \ud83e\udd75<\/h4>\n\n\n\n<p>Quant aux <strong>\u00e9quations du second degr\u00e9, elles prennent la forme ax\u00b2+bx+c=0 <\/strong>(avec a qui est non nul).&nbsp;La premi\u00e8re \u00e9tape consiste \u00e0 <strong>calculer le discriminant delta \u0394<\/strong>.&nbsp; Pour ce faire, il suffit d\u2019appliquer cette formule :<strong> \u0394 = b\u00b2 \u2013 4ac.<\/strong>&nbsp;<\/p>\n\n\n\n<p>Ensuite, selon le r\u00e9sultat, on va pouvoir en d\u00e9duire le nombre de solutions \u00e0 trouver. Petite pr\u00e9cision : le discriminant se voit en premi\u00e8re (sp\u00e9cialit\u00e9 maths), pas au coll\u00e8ge.<\/p>\n\n\n\n<p>\u274c Si \u0394 &lt; 0 : il n\u2019y a aucune solution.&nbsp;<\/p>\n\n\n\n<p>\ud83d\udc4d Ou alors, si \u0394 = 0 : il y a une seule solution qu\u2019on calculera avec<strong> x = -b\/2a<\/strong><\/p>\n\n\n\n<p>\ud83e\udd1eEt dernier cas de figure, si \u0394 &gt; 0 : il y a deux solutions qu\u2019on calculera avec <strong>x1 = (-b+\u221a\u0394)\/(2a) et x2 = (-b &#8211; \u221a\u0394)\/(2a)<\/strong>.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1Exemple<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Calculons le discriminant de l\u2019\u00e9quation 2x\u00b2 \u2212 x \u2212 6 = 0.<\/span><\/p>\n<p><span style=\"font-weight: 400\">On a donc, a = 2, b = -1 et c = -6\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Ce qui donne, \u0394 = b\u00b2 \u2212 4ac = (\u22121)\u00b2 \u2212 4 \u00d7 2 \u00d7 (\u22126) = 1 + 48 = 49. Comme \u0394 &gt; 0, l\u2019\u00e9quation poss\u00e8de deux solutions distinctes :\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">x1 = (\u2212(\u22121) + \u221a49) \/ (2 \u00d7 2<\/span>)<\/p>\n<p><span style=\"font-weight: 400\">= (1+7) \/ 4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= 8\/4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= 2\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">x2 = (\u2212(\u22121) \u2212 \u221a49) \/ (2 \u00d7 2<\/span>)<\/p>\n<p><span style=\"font-weight: 400\">= (1-7) \/ 4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= -6\/4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= -3\/2<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Voil\u00e0, les deux solutions de cette \u00e9quation du second degr\u00e9 sont : x1 = 2 et x2 = -3\/2.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>On a fait le tour des calculs litt\u00e9raux et de <strong>tous les th\u00e8mes que tu aborderas au cours de ton ann\u00e9e <\/strong>\ud83d\udcda ! Et si tu ne comprends toujours rien \u00e0 tout ce charabia, tu peux <a href=\"https:\/\/sherpas.com\/cours\/maths\">prendre des cours de maths avec les Sherpas<\/a> !<\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\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;265182&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;9&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;4.3&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;4.3\\\/5 - (9 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Calcul litt\u00e9ral : un monde sans chiffres \ud83d\ude2f !&quot;,&quot;width&quot;:&quot;122.2&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: 122.2px;\">\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            4.3\/5 - (9 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Toi qui pensais que les math\u00e9matiques n\u2019\u00e9taient que des calculs avec des chiffres et des nombres, d\u00e9sol\u00e9 de (&#8230;)<\/p>\n","protected":false},"author":356,"featured_media":265183,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[803,810],"tag":[77,770,79],"class_list":["post-265182","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-college","tag-fiche-revision","tag-lycee"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/265182","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\/356"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=265182"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/265182\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/265183"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=265182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=265182"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=265182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}