{"id":327,"date":"2023-07-06T07:19:13","date_gmt":"2023-07-06T07:19:13","guid":{"rendered":"https:\/\/mathority.org\/pt\/quadrado-de-uma-soma-ou-soma-ao-quadrado\/"},"modified":"2023-07-06T07:19:13","modified_gmt":"2023-07-06T07:19:13","slug":"quadrado-de-uma-soma-ou-soma-ao-quadrado","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/quadrado-de-uma-soma-ou-soma-ao-quadrado\/","title":{"rendered":"Quadrado de uma soma (ou soma ao quadrado)"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a f\u00f3rmula do quadrado de uma soma, ou seja, a identidade not\u00e1vel (a+b) <sup>2<\/sup> . Voc\u00ea tamb\u00e9m poder\u00e1 ver exemplos e exerc\u00edcios resolvidos de somas quadradas. E, al\u00e9m disso, voc\u00ea descobrir\u00e1 as propriedades geom\u00e9tricas escondidas neste not\u00e1vel produto. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-cuadrado-de-una-suma\"><\/span> Qual \u00e9 o quadrado de uma soma?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>quadrado de uma soma<\/strong> \u00e9 uma das identidades not\u00e1veis (ou produtos not\u00e1veis), portanto \u00e9 uma regra matem\u00e1tica que permite calcular rapidamente a pot\u00eancia de um bin\u00f4mio com dois termos positivos quadrados.<\/p>\n<p> Assim, o quadrado de uma soma consiste em dois termos diferentes somados e elevados ao quadrado, ou seja, a express\u00e3o alg\u00e9brica para o quadrado de uma soma \u00e9 <strong>(a+b) <sup>2<\/sup><\/strong> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-cuadrado-de-una-suma\"><\/span> F\u00f3rmula para o quadrado de uma soma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dada a defini\u00e7\u00e3o matem\u00e1tica deste not\u00e1vel tipo de identidade, veremos agora qual \u00e9 a <strong>f\u00f3rmula do quadrado de uma soma<\/strong> : <\/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-pour-le-carre-dune-somme.png\" alt=\"f\u00f3rmula para o quadrado de uma soma\" class=\"wp-image-2339\" width=\"269\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> De modo que o quadrado de uma soma \u00e9 igual ao quadrado do primeiro termo, mais o dobro do produto do primeiro pelo segundo, mais o quadrado do segundo.<\/p>\n<p> Assim, para resolver uma soma quadrada, n\u00e3o basta elevar cada adi\u00e7\u00e3o a dois, mas, al\u00e9m disso, as duas adi\u00e7\u00f5es devem ser multiplicadas entre si e por 2.<\/p>\n<p> \u00c9 importante lembrar disso, pois um erro muito comum na hora de somar os quadrados \u00e9 esquecer o produto entre os dois termos e calcular apenas os quadrados: <\/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\/polynomes-au-carre-dune-somme.jpg\" alt=\"quadrado de uma soma de polin\u00f4mios\" class=\"wp-image-2342\" width=\"246\" height=\"68\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Lembre-se de n\u00e3o deixar nenhum termo fora da f\u00f3rmula!<\/p>\n<p> Por outro lado, lembre-se que a f\u00f3rmula de uma subtra\u00e7\u00e3o ao quadrado (ou ao quadrado de uma subtra\u00e7\u00e3o) \u00e9 muito semelhante \u00e0 que acabamos de ver, mas tem uma diferen\u00e7a que muda completamente o resultado. Se voc\u00ea n\u00e3o tem certeza de como \u00e9 isso, voc\u00ea pode verificar aqui o que \u00e9 a f\u00f3rmula <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/quadrado-de-uma-diferenca-ou-subtracao\/\">de subtra\u00e7\u00e3o ao quadrado<\/a><\/span><\/strong> e como ela \u00e9 aplicada. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-cuadrados-de-sumas\"><\/span> Exemplos de soma quadrada<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Aqui est\u00e3o v\u00e1rios exemplos pr\u00e1ticos para que voc\u00ea possa ver como elevar ao quadrado uma soma:<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<ul>\n<li> Calcule a seguinte soma ao quadrado aplicando a f\u00f3rmula:<\/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-9a9b2aa575ef7fa83e8bb98cbb385ac8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+5)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A f\u00f3rmula para uma soma 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-e3c7bb69fbb939444db4e075615462f4_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> Devemos primeiro identificar os 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> 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> representa o<\/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> do par 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 5:<\/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-5ba75b0f34f956985ea0163011a03acf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a+b)^2\\\\[2ex] (x+5)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x \\\\[2ex] b=5 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bem, como agora sabemos 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-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> Podemos aplicar a f\u00f3rmula para encontrar o resultado do quadrado da soma: <\/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\/produits-notables-au-carre-dune-somme.jpg\" alt=\"quadrado de uma soma de produtos not\u00e1veis\" class=\"wp-image-2349\" width=\"284\" height=\"164\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<ul>\n<li> Resolva a seguinte express\u00e3o para o quadrado de uma soma:<\/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-12067275e14b98d59e004045606f26fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3x+4)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A f\u00f3rmula para o quadrado de uma soma \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-e3c7bb69fbb939444db4e075615462f4_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 neste problema<\/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> \u00e9 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-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p> E por outro lado,<\/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 o termo independente 4:<\/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-89bb3514fbd79ba368588655e152e9cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} a=3x \\\\[2ex] b=4 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Finalmente, uma vez identificados 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> , aplicamos a f\u00f3rmula da soma quadrada para resolver o produto not\u00e1vel: <\/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-ed0d9fcdbeeac2247b68789dd0268f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (3x+4)^2 &amp; =(3x)^2+2 \\cdot 3x\\cdot 4+4^2 \\\\[2ex] &amp; =9x^2+24x+16 \\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-suma\"><\/span> Prova da f\u00f3rmula do quadrado de uma soma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir deduziremos a f\u00f3rmula que acabamos de ver do quadrado de uma soma, para que voc\u00ea entenda de onde ela vem.<\/p>\n<p> Partindo de um bin\u00f4mio positivo elevado a 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-ef98ef741811c17cd99e75e5f848ea69_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> A pot\u00eancia acima \u00e9 obviamente equivalente ao 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-2cfde4aacc08aae1ed70fe5f7b2f74de_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-7b2df207ac593eaf04ac60ac40b89a7b_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> Ent\u00e3o, multiplicamos os dois par\u00eanteses usando 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-1c871c4ad6546c817128379acbef78c8_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=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Por fim, a partir dos termos resultantes, agrupamos aqueles que s\u00e3o semelhantes:<\/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-b645fb320040c599e077b3e5bdc4b407_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> E j\u00e1 chegamos na express\u00e3o polinomial da f\u00f3rmula, ent\u00e3o est\u00e1 provado:<\/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-66c4071b50f376018a8ac9b6f3f9f5fb_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> Embora possa ser dif\u00edcil de acreditar, a f\u00f3rmula do quadrado de uma soma tamb\u00e9m funciona para <a href=\"https:\/\/mathority.org\/pt\"><strong><span style=\"text-decoration: underline;\">fatorar polin\u00f4mios quadr\u00e1ticos<\/span><\/strong><\/a> . Caso voc\u00ea n\u00e3o saiba o que \u00e9, a fatora\u00e7\u00e3o polinomial \u00e9 um procedimento frequentemente usado em matem\u00e1tica para simplificar a express\u00e3o de um polin\u00f4mio. Descubra como isso \u00e9 feito clicando no link acima. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpretacion-geometrica-del-cuadrado-de-una-suma\"><\/span> Interpreta\u00e7\u00e3o geom\u00e9trica do quadrado de uma soma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> At\u00e9 agora vimos como o quadrado de uma soma \u00e9 calculado matematicamente, mas este produto not\u00e1vel tamb\u00e9m pode ser interpretado geometricamente.<\/p>\n<p> Observe o seguinte quadrado cujos lados medem <\/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-5f03f5d7b3d514b94a628f988975c108_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a+b:\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -2px;\"><\/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\/carre-geometrique-interpretation-d-une-somme.jpg\" alt=\"interpreta\u00e7\u00e3o geom\u00e9trica quadrada de uma soma\" class=\"wp-image-2364\" width=\"282\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> A \u00e1rea de um quadrado \u00e9 igual ao comprimento de um de seus lados ao quadrado. Portanto, como o lado do quadrado anterior \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-45dc37f5e6c04130e5e7cdc375a9fc8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a+b,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -4px;\"><\/p>\n<p> sua \u00e1rea (ou superf\u00edcie) \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-b02b123bc26be5152c4a9917a6cb9539_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>\n<p> Bem, como voc\u00ea pode ver na representa\u00e7\u00e3o quadrada, um quadrado com \u00e1rea 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-d3fbbc716a20a1a8e5fb339ee863ef14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\"><\/p>\n<p> ret\u00e2ngulos com duas \u00e1reas<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8d53cd0a9beed89b01eb3a3d6b7ff79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"ab,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\"><\/p>\n<p> e outro quadrado de superf\u00edcie<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3a795dbae63ac6ae2905fa73468f6dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p> Portanto, a f\u00f3rmula da soma de um quadrado tamb\u00e9m se cumpre do ponto de vista geom\u00e9trico: <\/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-e3c7bb69fbb939444db4e075615462f4_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-suma\"><\/span> Problemas resolvidos do quadrado de uma soma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir deixamos voc\u00eas com v\u00e1rios exerc\u00edcios de soma de quadrados resolvidos passo a passo para que voc\u00ea possa praticar e assim terminar de entender o conceito. Voc\u00ea pode nos escrever todas as suas perguntas nos coment\u00e1rios e teremos o maior prazer em respond\u00ea-las. \ud83d\udcad\ud83d\udcad\ud83d\udcad<\/p>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Determine as seguintes somas 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-9229e4ae2034182594cea6b72883a61e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x+3)^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-e9db6436020d25d8dde919b5db5071d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ (2+6x)^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-55d230fdf4d87dfb39f5427089c4bcd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(x^2+7\\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-8858ec9b4957c47679e682ab433bd75d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (5x+8y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" 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 resolver todas as identidades not\u00e1veis do problema basta aplicar a f\u00f3rmula do quadrado de uma soma: <\/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-e3c7bb69fbb939444db4e075615462f4_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-571dada676a093b9b625887a09615b5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}(x+3)^2&amp; =x^2+2\\cdot x\\cdot 3 +3^2\\\\[2ex] &amp; = \\bm{x^2+6x +9}\\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-8d696f9e8ea8a9246922a0aa132d7e24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}(2+6x)^2 &amp; =2^2+2\\cdot 2\\cdot 6x +(6x)^2\\\\[2ex] &amp; = \\bm{4+24x+36x^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-62f7ef68fc47d45958f6a10dbfe3f512_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned}\\left(x^2+7\\right)^2 &amp; = \\left(x^2\\right)^2+2\\cdot x^2\\cdot 7 +7^2\\\\[2ex] &amp; = \\bm{x^4+14x^2 +49}\\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-2fdf798e7d585cdbc2bbeb0417bfc62a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned}(5x+8y)^2 &amp; =(5x)^2+2\\cdot 5x\\cdot 8y +(8y)^2\\\\[2ex] &amp; = \\bm{25x^2+80xy+64y^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"331\" 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> Resolva a seguinte soma quadrada de dois termos 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-cde71610badce0bddaa952e68411ea3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(4x^2+2y^3\\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-097f1d298bc8e31ba41fc8163e310c6e_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-b432940794af539924a002fac6533134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\left(\\frac{4}{3}x^2+\\frac{3}{2}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 calcular todos os produtos not\u00e1veis do problema voc\u00ea deve usar a f\u00f3rmula da soma quadrada: <\/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-e3c7bb69fbb939444db4e075615462f4_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-b8eaa03c68adc376819c5e12081f6d39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}\\left(4x^2+2y^3\\right)^2 &amp; =\\left(4x^2\\right)^2+2\\cdot 4x^2\\cdot 2y^3 +\\left(2y^3\\right)^2\\\\[2ex] &amp; = \\bm{16x^4+16x^2y^3+4y^6}\\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\"> Na 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-a38b1df7ca331cb002253d52eb008608_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{18x}\\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 soma ao quadrado possuem coeficientes fracion\u00e1rios, ent\u00e3o para resolv\u00ea-lo tamb\u00e9m 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-c50dcca740e334b34f746e71f4af826e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\begin{aligned} \\left(\\frac{4}{3}x^2+\\frac{3}{2}x\\right)^2 &amp; = \\left(\\frac{4}{3}x^2\\right)^2+2\\cdot \\frac{4}{3}x^2\\cdot \\frac{3}{2}x +\\left(\\frac{3}{2}x\\right)^2\\\\[2ex] &amp; = \\frac{4^2}{3^2}x^4+2\\cdot \\frac{12}{6}x^3 +\\frac{3^2}{2^2}x^2 \\\\[2ex] &amp;= \\frac{16}{9}x^4 +2\\cdot 2x^3+\\frac{9}{4}x^2 \\\\[2ex] &amp; = \\mathbf{\\frac{16}{9}} \\bm{x^4+4x^3+}\\mathbf{\\frac{9}{4}}\\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<h3 class=\"wp-block-heading\">Exerc\u00edcio 3<\/h3>\n<p> Encontre a seguinte pot\u00eancia aplicando a f\u00f3rmula do quadrado de uma soma e sem usar a calculadora: <\/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-86db45137cb4792d046d171c28662c90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"17^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\"><\/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\"> Em primeiro lugar, o n\u00famero dezassete pode ser dividido na soma de 10 mais 7:<\/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-55dc7f45d8d495163afd5d22d2c612ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"17^2=(10+7)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ent\u00e3o convertemos a pot\u00eancia para uma soma quadrada. Portanto, podemos agora aplicar a f\u00f3rmula correspondente:<\/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-83e35048f0ae6ae12bc2b5b3d761fb99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(10+7)^2 &amp; = 10^2+2\\cdot 10 \\cdot 7 +7^2 \\\\[2ex] &amp; =100+140+49\\\\[2ex] &amp; =289 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"238\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Resumindo, o resultado da potencializa\u00e7\u00e3o \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-d13bfdf83060795d27403604f251047d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"17^2=\\bm{289}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Como voc\u00ea viu neste exerc\u00edcio, a f\u00f3rmula da soma quadrada tamb\u00e9m \u00e9 \u00fatil para calcular pot\u00eancias de n\u00fameros grandes sem usar uma calculadora. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cuadrado-de-una-suma-de-3-terminos\"><\/span> Quadrado de uma soma de 3 termos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00c0s vezes podemos descobrir que precisamos resolver o quadrado de tr\u00eas termos adicionados, ou seja, (a+b+c) <sup>2<\/sup> . Logicamente, nestes casos n\u00e3o podemos utilizar a f\u00f3rmula que explicamos, pois dentro dos par\u00eanteses temos um trin\u00f4mio em vez de um bin\u00f4mio. Portanto, \u00e9 necess\u00e1rio usar uma f\u00f3rmula diferente.<\/p>\n<p> A <strong>f\u00f3rmula do quadrado da soma de 3 termos<\/strong> \u00e9 a seguinte:<\/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-547cbf526b192d07d188c703a68f12e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{blauquadreejemplo}{HTML}{ff5733}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=blauquadreejemplo,      boxrule=1.2pt, boxsep=2.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2.5mm}{-2.5mm}{0mm}{blauquadreejemplo!20!white,} ]}]{equation*}     (a+b+c)^2 = a^2+2a(b+c)+b^2+2bc+c^2 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"294\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Vamos ver como esta f\u00f3rmula \u00e9 aplicada atrav\u00e9s de um exemplo:<\/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-d0816bbe156553fc1ef5920ac2b2e09f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (2x+3y+5)^2 &amp; = (2x)^2 + 2\\cdot 2x (3y+5)+(3y)^2+2\\cdot  3y \\cdot 5 + 5^2 \\\\[2ex] &amp; =4x^2 +4x (3y+5)+9y^2+30y +25 \\\\[2ex] &amp;=4x^2 +12xy+20x+9y^2+30y +25 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"481\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Como voc\u00ea pode ver, adicionar um elemento \u00e0 f\u00f3rmula torna o resultado muito mais complicado.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a f\u00f3rmula do quadrado de uma soma, ou seja, a identidade not\u00e1vel (a+b) 2 . Voc\u00ea tamb\u00e9m poder\u00e1 ver exemplos e exerc\u00edcios resolvidos de somas quadradas. E, al\u00e9m disso, voc\u00ea descobrir\u00e1 as propriedades geom\u00e9tricas escondidas neste not\u00e1vel produto. Qual \u00e9 o quadrado de uma soma? O quadrado de uma soma \u00e9 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/quadrado-de-uma-soma-ou-soma-ao-quadrado\/\"> <span class=\"screen-reader-text\">Quadrado de uma soma (ou soma ao quadrado)<\/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-327","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 soma (ou soma ao quadrado) - 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-soma-ou-soma-ao-quadrado\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quadrado de uma soma (ou soma ao quadrado) - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a f\u00f3rmula do quadrado de uma soma, ou seja, a identidade not\u00e1vel (a+b) 2 . Voc\u00ea tamb\u00e9m poder\u00e1 ver exemplos e exerc\u00edcios resolvidos de somas quadradas. E, al\u00e9m disso, voc\u00ea descobrir\u00e1 as propriedades geom\u00e9tricas escondidas neste not\u00e1vel produto. Qual \u00e9 o quadrado de uma soma? 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