{"id":338,"date":"2023-07-06T04:01:11","date_gmt":"2023-07-06T04:01:11","guid":{"rendered":"https:\/\/mathority.org\/pt\/soma-de-cubos\/"},"modified":"2023-07-06T04:01:11","modified_gmt":"2023-07-06T04:01:11","slug":"soma-de-cubos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/soma-de-cubos\/","title":{"rendered":"Soma dos cubos"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a f\u00f3rmula da soma dos cubos e a explica\u00e7\u00e3o de como as somas dos cubos s\u00e3o fatoradas. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos e exerc\u00edcios resolvidos de somas de cubos. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-suma-de-cubos\"><\/span>Qual \u00e9 a soma dos cubos?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>soma dos cubos<\/strong> \u00e9 um bin\u00f4mio (polin\u00f4mio com apenas dois mon\u00f4mios) cujos dois termos s\u00e3o positivos e, al\u00e9m disso, suas ra\u00edzes c\u00fabicas s\u00e3o exatas. Portanto, a express\u00e3o alg\u00e9brica para uma soma de cubos \u00e9 <strong>a <sup>3<\/sup> +b <sup>3<\/sup><\/strong> .<\/p>\n<p> Al\u00e9m disso, a soma dos cubos perfeitos corresponde a um produto not\u00e1vel (ou identidade not\u00e1vel), o que significa que existe uma f\u00f3rmula para resolv\u00ea-lo diretamente, sem fazer muitos c\u00e1lculos. A seguir veremos como isso \u00e9 feito. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-suma-de-cubos\"><\/span> F\u00f3rmula da soma dos cubos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o matem\u00e1tica da soma dos cubos, vamos agora ver qual \u00e9 a f\u00f3rmula da soma dos cubos: <\/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-de-la-somme-des-cubes.png\" alt=\"f\u00f3rmula da soma dos cubos\" class=\"wp-image-2663\" width=\"306\" height=\"307\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Assim, a soma de dois termos ao cubo \u00e9 igual \u00e0 soma destes dois termos multiplicada pelo quadrado do primeiro termo, menos o produto das duas quantidades, mais o quadrado do segundo termo.<\/p>\n<p> Portanto, quando aplicamos a f\u00f3rmula da soma dos cubos perfeitos, estamos na verdade fatorando um polin\u00f4mio, pois estamos convertendo a express\u00e3o de um polin\u00f4mio em um produto de dois fatores. Se voc\u00ea ainda n\u00e3o tem certeza do que significa fatorar um polin\u00f4mio, recomendamos que veja como <a href=\"https:\/\/mathority.org\/pt\"><strong><span style=\"text-decoration: underline;\">fatorar polin\u00f4mios<\/span><\/strong><\/a> antes de continuar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-factorizaciones-de-sumas-de-cubos\"><\/span> Exemplos de fatora\u00e7\u00e3o de somas de cubos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o do conceito de soma de cubos perfeitos, veremos v\u00e1rios exemplos de fatora\u00e7\u00e3o de somas de cubos utilizando a f\u00f3rmula:<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<ul>\n<li> Fatore a seguinte soma de cubos usando 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-51a33d4fd52d94afa78abd4be81cf7f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"48\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Na verdade, \u00e9 uma soma de cubos porque a raiz c\u00fabica do mon\u00f4mio<\/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-a5e0e31e823b4d5c9a90c0d01d5e8fcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 exato (n\u00e3o fornece n\u00famero decimal) e o n\u00famero 8 tamb\u00e9m: <\/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-1105a3d4349d8c5d3eae7b16dc079ef1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{x^3} = x\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -1px;\"><\/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-71ce4de717d54a2fb6c3282de038913a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{8} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -2px;\"><\/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-4171629bd68508074adfbf81cf982b5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+8=x^3+2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Portanto, podemos aplicar a f\u00f3rmula da soma de cubos para transformar a express\u00e3o c\u00fabica em um produto de um bin\u00f4mio e um trin\u00f4mio:<\/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-261e42482dc7545bb617e1d662dd2cc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+b^3  = (a+b)(a^2-ab+b^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" 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-62bca2a2972fa58da86d3a6dca21e62e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3 +2^3 = (x+2)(x^2-x \\cdot 2 + 2^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"257\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> E, por fim, s\u00f3 nos resta resolver a multiplica\u00e7\u00e3o e a pot\u00eancia:<\/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-0993ec317132eea25d3144b4f2fe61f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3 +2^3 = (x+2)(x^2-2x + 4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Se observarmos atentamente a express\u00e3o obtida, gra\u00e7as \u00e0 f\u00f3rmula da soma dos cubos podemos facilmente <a href=\"https:\/\/mathority.org\/pt\/raizes-de-um-polinomio\/\"><strong><span style=\"text-decoration: underline;\">encontrar a raiz de um polin\u00f4mio<\/span><\/strong><\/a> . Neste caso, uma das ra\u00edzes do polin\u00f4mio seria<\/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-86f872935a384592f05d5fdc077a0a0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-2.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<p> Por\u00e9m, para encontrar todas as ra\u00edzes (ou zeros) de um polin\u00f4mio, \u00e9 necess\u00e1rio seguir um procedimento mais complicado, descubra como na p\u00e1gina vinculada.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<ul>\n<li> Fatore o seguinte bin\u00f4mio aplicando a f\u00f3rmula da soma dos cubos perfeitos.<\/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-98f53ef4a4c3c39ecc0682c8d3df7666_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> O polin\u00f4mio neste exemplo tamb\u00e9m consiste em uma soma de cubos porque tanto a raiz c\u00fabica do mon\u00f4mio<\/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-1f61617ac46da6980b038f6068280293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<p> do termo independente 1 s\u00e3o exatos: <\/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-ff524d796280c6890e586ebb8a8023e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{8x^3} = 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -1px;\"><\/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-9f8402a5e8c6e7baa1ee3f973126c38f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{1} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -2px;\"><\/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-a4be4848c5fb1c048ff19989f177b944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+1 =(2x)^3+1^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"159\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Podemos, portanto, usar a f\u00f3rmula da soma dos cubos perfeitos para simplificar a express\u00e3o:<\/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-261e42482dc7545bb617e1d662dd2cc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+b^3  = (a+b)(a^2-ab+b^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" 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-12bb382af2a96841b698c579bd102e82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x)^3+1^3 = (2x+1)\\bigl((2x)^2-2x \\cdot 1 + 1^2\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"320\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Por fim, basta calcular as opera\u00e7\u00f5es resultantes:<\/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-7915cecea88607cdc34ea9c53e25654c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x)^3+1^3 = (2x+1)(4x^2-2x + 1\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"276\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Agora que voc\u00ea viu como resolver uma soma de cubos, talvez queira saber como fatorar uma <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/subtracao-de-diferenca-de-cubos\/\">diferen\u00e7a de cubos<\/a><\/span><\/strong> . Porque embora a f\u00f3rmula da diferen\u00e7a de cubos seja semelhante, tem uma pequena altera\u00e7\u00e3o que nos permite distinguir entre uma soma e uma diferen\u00e7a de cubos. Deixamos este link para que voc\u00ea possa ver em que consiste essa mudan\u00e7a significativa e como \u00e9 calculada uma subtra\u00e7\u00e3o de cubos. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-sumas-de-cubos\"><\/span> Problemas resolvidos de somas de cubos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Fatore a seguinte adi\u00e7\u00e3o de cubos com 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-64ab426c17c8571c1726998770c4b202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^6+27x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -2px;\"><\/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\"> A express\u00e3o corresponde a uma soma de cubos porque as ra\u00edzes c\u00fabicas dos dois elementos do polin\u00f4mio s\u00e3o exatas: <\/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-4940d2f98a52cbec3af20836bd69d3b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{x^6} = x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"72\" style=\"vertical-align: -1px;\"><\/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-c60bf4d19507d04bdae93d067a8d693d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{27x^3} = 3x\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"92\" style=\"vertical-align: -1px;\"><\/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-1e8dbe7c909416a5a330d21440a3b89a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^6+27x^3=\\bigl(x^2\\bigr)^3+(3x)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"202\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Portanto, podemos usar a f\u00f3rmula da soma de cubos perfeitos para fatorar a express\u00e3o c\u00fabica em um produto de um bin\u00f4mio e um trin\u00f4mio: <\/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-261e42482dc7545bb617e1d662dd2cc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+b^3  = (a+b)(a^2-ab+b^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" 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-26d11de6c65531d48077d92ffb61bfcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(x^2\\bigr)^3+(3x)^3 = \\left(x^2+3x\\right)\\left( \\left(x^2\\right)^2-x^2 \\cdot 3x + (3x)^2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"397\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Com o qual resolvemos todas as opera\u00e7\u00f5es para encontrar o polin\u00f4mio fatorado: <\/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-326b49aeb6e6835bd07aad5e4981b0f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(x^2\\bigr)^3+(3x)^3 = \\left(x^2+3x\\right)\\left( x^4-3x^3 + 9x^2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"332\" style=\"vertical-align: -7px;\"><\/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> Expresse cada produto como uma soma de cubos: <\/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-52faab57ad4a1ac55f7bfef5b1b8f45c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x+5)(x^2-5x+25)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"192\" 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-d8ffa443eb8d1c0e020249e47f8b0d3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ (2x+7)(4x^2-14x+49)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" 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-80cc39921b76e54197953588ddf19544_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ (8x+y^2)(64x^2-8xy^2+y^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"242\" 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\"> As express\u00f5es dos 3 exerc\u00edcios respeitam a f\u00f3rmula da soma dos cubos, portanto \u00e9 suficiente resolver as multiplica\u00e7\u00f5es dos polin\u00f4mios: <\/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-db8da16c852b5b0b6c5b713c0d2d4fcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{array}{l}(x+5)(x^2-5x+25) = \\\\[2ex] = x^3-5x^2+25x+5x^2-25x+125 = \\\\[2ex] = x^3 +125\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"339\" 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-73ca58a006b5e2fd30f9e2bc1fe170f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{array}{l}(2x+7)(4x^2-14x+49) = \\\\[2ex] =  8x^3-28x^2+98x+28x^2-98x+343 = \\\\[2ex]  = 8x^3+343\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"364\" 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-fcad6960f7a6c30cc8f251d33ed98a5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{array}{l}(8x+y^2)(64x^2-8xy^2+y^4) = \\\\[2ex] =512x^3-64x^2y^2+8xy^4+64x^2y^2-8xy^4+y^6= \\\\[2ex] = 512x^3+y^6\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"423\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Se voc\u00ea se interessa mais por identidades not\u00e1veis, saiba que existe uma que muita gente esquece (e \u00e9 muito usada). Mas \u00e9 importante lembrar a f\u00f3rmula para esta identidade not\u00e1vel, chamada <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/trinomio-ao-quadrado\/\">trin\u00f4mio ao quadrado<\/a><\/span><\/strong> . \u00c9 por isso que deixamos este link onde voc\u00ea poder\u00e1 ver o que \u00e9 e como esta f\u00f3rmula \u00e9 aplicada.<\/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 da soma dos cubos e a explica\u00e7\u00e3o de como as somas dos cubos s\u00e3o fatoradas. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos e exerc\u00edcios resolvidos de somas de cubos. Qual \u00e9 a soma dos cubos? A soma dos cubos \u00e9 um bin\u00f4mio (polin\u00f4mio com apenas dois mon\u00f4mios) cujos dois &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\"> <span class=\"screen-reader-text\">Soma dos cubos<\/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-338","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>Soma dos cubos - Mathority<\/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\/soma-de-cubos\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Soma dos cubos - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a f\u00f3rmula da soma dos cubos e a explica\u00e7\u00e3o de como as somas dos cubos s\u00e3o fatoradas. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos e exerc\u00edcios resolvidos de somas de cubos. Qual \u00e9 a soma dos cubos? A soma dos cubos \u00e9 um bin\u00f4mio (polin\u00f4mio com apenas dois mon\u00f4mios) cujos dois &hellip; Soma dos cubos Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T04:01:11+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-la-somme-des-cubes.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Soma dos cubos\",\"datePublished\":\"2023-07-06T04:01:11+00:00\",\"dateModified\":\"2023-07-06T04:01:11+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\"},\"wordCount\":748,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Identidades not\u00e1veis\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/soma-de-cubos\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\",\"url\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\",\"name\":\"Soma dos cubos - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-07-06T04:01:11+00:00\",\"dateModified\":\"2023-07-06T04:01:11+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/soma-de-cubos\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/soma-de-cubos\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Soma dos cubos\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Soma dos cubos - Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/soma-de-cubos\/","og_locale":"pt_BR","og_type":"article","og_title":"Soma dos cubos - Mathority","og_description":"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a f\u00f3rmula da soma dos cubos e a explica\u00e7\u00e3o de como as somas dos cubos s\u00e3o fatoradas. 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