{"id":329,"date":"2023-07-06T06:56:12","date_gmt":"2023-07-06T06:56:12","guid":{"rendered":"https:\/\/mathority.org\/pt\/quadrado-de-uma-diferenca-ou-subtracao\/"},"modified":"2023-07-06T06:56:12","modified_gmt":"2023-07-06T06:56:12","slug":"quadrado-de-uma-diferenca-ou-subtracao","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/quadrado-de-uma-diferenca-ou-subtracao\/","title":{"rendered":"Quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o)"},"content":{"rendered":"<p>Aqui explicamos o que \u00e9 a f\u00f3rmula de identidade not\u00e1vel do quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o), ou seja, mostramos como se resolve a express\u00e3o (ab) <sup>2<\/sup> . Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e praticar com exerc\u00edcios resolvidos no quadrado da diferen\u00e7a. E por fim, mostramos a demonstra\u00e7\u00e3o da f\u00f3rmula e a interpreta\u00e7\u00e3o geom\u00e9trica deste not\u00e1vel tipo de produto. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-cuadrado-de-una-diferencia-o-resta\"><\/span> Qual \u00e9 o quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o)?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>quadrado de uma diferen\u00e7a<\/strong> , ou <strong>quadrado de uma subtra\u00e7\u00e3o<\/strong> , \u00e9 uma das <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/identidades-produtos-igualdades-notaveis-exercicios-resolvidos\/\">identidades not\u00e1veis<\/a><\/span><\/strong> (ou produtos not\u00e1veis), ou seja, consiste em uma regra matem\u00e1tica que facilita o c\u00e1lculo da quadratura de um bin\u00f4mio com dois termos: um positivo e o outro negativo.<\/p>\n<p> Portanto, a express\u00e3o alg\u00e9brica para o quadrado de uma diferen\u00e7a \u00e9 <strong>(ab) <sup>2<\/sup><\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-cuadrado-de-una-diferencia-o-resta\"><\/span> F\u00f3rmula para o quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o deste tipo de identidade not\u00e1vel, veremos como resolver o quadrado de uma diferen\u00e7a com sua f\u00f3rmula: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-du-carre-dune-difference-ou-soustraction.png\" alt=\"f\u00f3rmula para o quadrado de uma diferen\u00e7a ou subtra\u00e7\u00e3o\" class=\"wp-image-2407\" width=\"299\" height=\"300\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <strong>Assim, o quadrado de uma diferen\u00e7a \u00e9 igual ao quadrado do primeiro termo, menos o dobro do produto do primeiro pelo segundo, mais o quadrado do segundo.<\/strong><\/p>\n<p> Portanto, para calcular uma diferen\u00e7a ou uma subtra\u00e7\u00e3o quadrada, voc\u00ea n\u00e3o deve apenas elevar cada termo a dois, mas tamb\u00e9m multiplic\u00e1-los entre si e por 2.<\/p>\n<p> \u00c9 importante lembrar disso, pois um erro muito comum na subtra\u00e7\u00e3o de quadrados \u00e9 n\u00e3o colocar o produto entre os dois termos e apenas resolver o quadrado da diminui\u00e7\u00e3o e a subtra\u00e7\u00e3o da subtra\u00e7\u00e3o: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-du-binome-d-une-soustraction.jpg\" alt=\"quadrado do bin\u00f4mio de uma subtra\u00e7\u00e3o\" class=\"wp-image-2409\" width=\"235\" height=\"66\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> N\u00e3o se esque\u00e7a do produto entre a e b! <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-cuadrados-de-diferencias-o-restas\"><\/span> Exemplos de quadrados de diferen\u00e7a (ou subtra\u00e7\u00e3o)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a f\u00f3rmula do quadrado da diferen\u00e7a, podemos fazer c\u00e1lculos com ela. E para que voc\u00ea possa ver como isso \u00e9 feito, preparamos v\u00e1rios exemplos resolvidos do quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o).<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<ul>\n<li> Resolva a seguinte diferen\u00e7a ao quadrado:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c639502958a3e7b758e74eda141cd322_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-3)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00c9 uma subtra\u00e7\u00e3o ao quadrado, ent\u00e3o voc\u00ea deve aplicar sua f\u00f3rmula:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, devemos identificar quais s\u00e3o os valores das inc\u00f3gnitas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> da f\u00f3rmula. Nesse caso,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a vari\u00e1vel<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> corresponde ao n\u00famero 3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1bb2d14a30d2cdabae6458f5df32392a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a-b)^2\\\\[2ex] (x-3)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x \\\\[2ex] b=3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Observe que o sinal negativo n\u00e3o faz parte de<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a521efcd0a946cd643aebe98b5b41a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> mas voc\u00ea deve sempre pegar o n\u00famero sem o sinal para aplicar corretamente a f\u00f3rmula.<\/p>\n<p> Portanto, j\u00e1 conhecemos os valores de<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> e de<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> Portanto, precisamos apenas substituir esses valores na f\u00f3rmula: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome-dune-soustraction-au-carre-exercices-resolus.jpg\" alt=\"exerc\u00edcios de subtra\u00e7\u00e3o binomial de um quadrado resolvidos\" class=\"wp-image-2417\" width=\"299\" height=\"173\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<ul>\n<li> Calcule o seguinte bin\u00f4mio de uma subtra\u00e7\u00e3o quadrada:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a94d5ee509fb5d8e9eaf9a633f36f46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(5x-2)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A f\u00f3rmula para a diferen\u00e7a quadrada \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, primeiro precisamos identificar os valores de<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> e de<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> da f\u00f3rmula. Neste problema,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> representa o mon\u00f4mio<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6093d29b7c98d4d53162882fe6703e10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 equivalente ao termo independente do bin\u00f4mio, ou seja, 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-868a41eb665f5bc94959448547c060d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a-b)^2\\\\[2ex] (5x-2)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=5x \\\\[2ex] b=2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Finalmente, uma vez que sabemos o valor dos par\u00e2metros<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> , simplesmente aplicamos a f\u00f3rmula binomial para subtra\u00e7\u00e3o ao quadrado: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5e88231a654b23a306e53e17d175d25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (5x-2)^2 &amp; = (5x)^2-2\\cdot 5x \\cdot 2 + 2^2 \\\\[2ex] &amp; = 25x^2-20x+4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"256\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-cuadrado-de-una-diferencia\"><\/span> Prova da f\u00f3rmula do quadrado de uma diferen\u00e7a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Deduziremos ent\u00e3o de onde vem a f\u00f3rmula do quadrado de uma subtra\u00e7\u00e3o. Embora voc\u00ea n\u00e3o precise memorizar a prova, ainda \u00e9 bom entender a matem\u00e1tica por tr\u00e1s dela.<\/p>\n<p> Se partirmos da express\u00e3o do bin\u00f4mio de todas as subtra\u00e7\u00f5es:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f88949b2f3fcc20e9d00f495e471cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Obviamente, a pot\u00eancia anterior \u00e9 igual ao produto do fator<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ab5e2adaf0a63382c066ea55b51147c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<p> multiplicado por si mesmo:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5786e5179724339feaef50ccdb33ead1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2= (a-b)\\cdot (a-b)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora multiplicamos os dois par\u00eanteses aplicando a propriedade distributiva:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b46073fd758d93fff8956f0a8dd57af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(a-b)\\cdot (a-b) &amp; = a\\cdot a +a\\cdot (-b) - b\\cdot a - b \\cdot (-b) \\\\[2ex] &amp; = a^2-ab-ba+b^2 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> E s\u00f3 temos que agrupar termos semelhantes para terminar de provar a f\u00f3rmula:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68a1e26dd180891fc1ee31584a471ca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2-ab-ba+b^2 = a^2-2ab +b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"256\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Para que a f\u00f3rmula do quadrado de uma subtra\u00e7\u00e3o seja provada matematicamente:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A t\u00edtulo de curiosidade, a expans\u00e3o da express\u00e3o binomial de uma subtra\u00e7\u00e3o quadrada tamb\u00e9m \u00e9 conhecida como trin\u00f4mio quadrado perfeito. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpretacion-geometrica-del-cuadrado-de-una-diferencia\"><\/span> Interpreta\u00e7\u00e3o geom\u00e9trica do quadrado de uma diferen\u00e7a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o da no\u00e7\u00e3o de quadrado de uma diferen\u00e7a, veremos como interpretar geometricamente esta not\u00e1vel igualdade.<\/p>\n<p> Observe o seguinte quadrado com lados de comprimento <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fad90838c7fa310bdbea2364787ced6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/interpretation-geometrique-du-carre-de-la-difference.jpg\" alt=\"interpreta\u00e7\u00e3o geom\u00e9trica do quadrado de uma diferen\u00e7a\" class=\"wp-image-2427\" width=\"321\" height=\"321\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> A \u00e1rea (ou \u00e1rea de superf\u00edcie) de um quadrado ou ret\u00e2ngulo \u00e9 calculada multiplicando dois de seus lados adjacentes. Portanto, a \u00e1rea de todo o quadrado inteiro acima \u00e9<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-217fa12aa2b62c902c84fa81b873991a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\\cdot a = a^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\"><\/p>\n<p> Da mesma forma, a \u00e1rea de cada ret\u00e2ngulo amarelo \u00e9 igual a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6598b0081ed8a7b827b59324acfae35a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\\cdot b = ab.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<p> E finalmente, o pequeno quadrado mostrado no canto superior direito tem uma \u00e1rea de<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4eeba14a61903733ce2d13bcf35d3ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\\cdot b =b^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Isto significa que um quadrado de lado<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62727d3bc0a05c70472ae09eba377396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b),\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<p> cuja superf\u00edcie \u00e9<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff46b79cf0127ee95c26509e5c5c957c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -5px;\"><\/p>\n<p> pode ser decomposto na \u00e1rea de um quadrado de dimens\u00e3o<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8fa4ffebd0bdc66a5e68aa7b712f46c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> menos 2 vezes a \u00e1rea de um ret\u00e2ngulo de dimens\u00f5es<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> , mais a \u00e1rea de um quadrado lateral<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf59029b62b61185814b66fa6004b2f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> Resumindo, a f\u00f3rmula do quadrado de uma diferen\u00e7a tamb\u00e9m pode ser verificada geometricamente: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-cuadrado-de-una-diferencia-o-resta\"><\/span> Problemas resolvidos do quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea possa praticar, deixamos v\u00e1rios exerc\u00edcios resolvidos passo a passo sobre o produto not\u00e1vel do quadrado de uma diferen\u00e7a. Lembre-se de que voc\u00ea pode nos escrever qualquer d\u00favida abaixo nos coment\u00e1rios.<\/p>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Resolva as seguintes subtra\u00e7\u00f5es ao quadrado: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c11a4f53553874acb14ec9bbd0c78d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x-2)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55330f15a13171e004a6fd9063b5042d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ (3-7x)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a9afedffeffbe27f4e9c5d94b2bcad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(x^2-6\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"100\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f96b2af0d8ddde63f0f5ff04acde9e8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (-3x+y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d4b37f1b9fc0170cdcdf8ff4a136e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ (4x-3y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para encontrar todas as identidades not\u00e1veis do problema, basta aplicar a f\u00f3rmula do quadrado de uma diferen\u00e7a, que \u00e9: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14d502eda968fe82617b4403cd9c4722_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}(x-2)^2&amp; =x^2-2\\cdot x\\cdot 2 +2^2\\\\[2ex] &amp; = \\bm{x^2-4x +4}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"248\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c22d520301280872e645f5683a2fba8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}(3-7x)^2 &amp; =3^2-2\\cdot 3\\cdot 7x +(7x)^2\\\\[2ex] &amp; = \\bm{9-42x+49x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"288\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-95c7c481a96b20b700bd2253c90f0c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned}\\left(x^2-6\\right)^2 &amp; = \\left(x^2\\right)^2-2\\cdot x^2\\cdot 6 +6^2\\\\[2ex] &amp; = \\bm{x^4-12x^2 +36}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"66\" width=\"290\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3cea9fa89580d3d9d9df7fd93cca2b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned}(-3x+y)^2 &amp; = (y-3x)^2 \\\\[2ex] &amp; = y^2-2\\cdot y\\cdot 3x +(3x)^2\\\\[2ex] &amp; = \\bm{y^2-6yx+9x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"304\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-138b359ce2e8f8b1012c6ecf1b7fb9b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ \\begin{aligned}(4x-3y)^2 &amp; = (4x)^2-2\\cdot 4x\\cdot 3y +(3y)^2\\\\[2ex] &amp; = \\bm{16x^2-24xy+9y^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"329\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 2<\/h3>\n<p> Determine os seguintes quadrados das diferen\u00e7as de duas quantidades aplicando a f\u00f3rmula: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2d817b4488d40c395b508191a9257bf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(6x^3-4y^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"127\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b93817974b7ab8b03fa60852c85e570a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\displaystyle \\left(\\sqrt{2x}-\\sqrt{8x}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"146\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ce347a33830b600df805f9b3089a629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\left(\\frac{5}{2}x^2-\\frac{4}{5}x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"137\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para determinar todos os produtos not\u00e1veis do problema \u00e9 necess\u00e1rio usar a f\u00f3rmula de subtra\u00e7\u00e3o ao quadrado: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73b9ba584f955a0cae5564a2226d465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}\\left(6x^3-4y^4\\right)^2 &amp; =\\left(6x^3\\right)^2-2\\cdot 6x^3\\cdot 4y^4 +\\left(4y^4\\right)^2\\\\[2ex] &amp; = \\bm{36x^6-48x^3y^4+16y^8}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Para resolver a se\u00e7\u00e3o B), voc\u00ea precisa lembrar que se uma raiz for quadrada, ela ser\u00e1 simplificada:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-38cd9e9855f7f79f607247ccc731e297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(\\sqrt{2x}-\\sqrt{8x}\\right)^2 &amp; =\\left(\\sqrt{2x}\\right)^2-2\\cdot \\sqrt{2x}\\cdot \\sqrt{8x} +\\left(\\sqrt{8x}\\right)^2\\\\[2ex] &amp; =2x-2\\sqrt{2x\\cdot 8x} +8x \\\\[2ex] &amp; = 10x-2\\sqrt{16x^2} \\\\[2ex] &amp;= 10x-2\\cdot 4x = \\\\[2ex] &amp; = 10x -8x \\\\[2ex] &amp; = \\bm{2x}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"247\" width=\"443\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Os mon\u00f4mios da \u00faltima subtra\u00e7\u00e3o ao quadrado possuem coeficientes fracion\u00e1rios, ent\u00e3o para resolv\u00ea-lo precisamos usar as propriedades das fra\u00e7\u00f5es: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46106420913cc7a370e2f5215af0f2a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\begin{aligned} \\left(\\frac{5}{2}x^2-\\frac{4}{5}x\\right)^2 &amp; = \\left(\\frac{5}{2}x^2\\right)^2-2\\cdot \\frac{5}{2}x^2\\cdot \\frac{4}{5}x +\\left(\\frac{4}{5}x\\right)^2\\\\[2ex] &amp; = \\frac{5^2}{2^2}x^4-2\\cdot \\frac{20}{10}x^3 +\\frac{4^2}{5^2}x^2 \\\\[2ex] &amp;= \\frac{25}{4}x^4 -2\\cdot 2x^3+\\frac{16}{25}x^2 \\\\[2ex] &amp; = \\mathbf{\\frac{25}{4}} \\bm{x^4-4x^3+}\\mathbf{\\frac{16}{25}}\\bm{x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"416\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Aqui explicamos o que \u00e9 a f\u00f3rmula de identidade not\u00e1vel do quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o), ou seja, mostramos como se resolve a express\u00e3o (ab) 2 . Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e praticar com exerc\u00edcios resolvidos no quadrado da diferen\u00e7a. E por fim, mostramos a demonstra\u00e7\u00e3o da f\u00f3rmula e a interpreta\u00e7\u00e3o geom\u00e9trica &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/quadrado-de-uma-diferenca-ou-subtracao\/\"> <span class=\"screen-reader-text\">Quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o)<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[15],"tags":[],"class_list":["post-329","post","type-post","status-publish","format-standard","hentry","category-identidades-notaveis"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o) - Matoridade<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/quadrado-de-uma-diferenca-ou-subtracao\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o) - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Aqui explicamos o que \u00e9 a f\u00f3rmula de identidade not\u00e1vel do quadrado de uma diferen\u00e7a (ou subtra\u00e7\u00e3o), ou seja, mostramos como se resolve a express\u00e3o (ab) 2 . 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