{"id":341,"date":"2023-07-06T03:17:32","date_gmt":"2023-07-06T03:17:32","guid":{"rendered":"https:\/\/mathority.org\/pt\/subtracao-de-diferenca-de-cubos\/"},"modified":"2023-07-06T03:17:32","modified_gmt":"2023-07-06T03:17:32","slug":"subtracao-de-diferenca-de-cubos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/subtracao-de-diferenca-de-cubos\/","title":{"rendered":"Diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos"},"content":{"rendered":"<p>Nesta p\u00e1gina explicamos como fatorar uma diferen\u00e7a de cubos (f\u00f3rmula). Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos e at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-diferencia-de-cubos\"><\/span> Qual \u00e9 a diferen\u00e7a entre cubos?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em matem\u00e1tica, a <strong>diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos<\/strong> \u00e9 um bin\u00f4mio (polin\u00f4mio com apenas dois mon\u00f4mios) composto por um termo positivo e um termo negativo cujas ra\u00edzes c\u00fabicas s\u00e3o exatas. Em outras palavras, a express\u00e3o alg\u00e9brica para uma diferen\u00e7a de cubos \u00e9 <strong>a <sup>3<\/sup> -b <sup>3<\/sup><\/strong> .<\/p>\n<p> Da mesma forma, a diferen\u00e7a em cubos perfeitos corresponde a um produto not\u00e1vel. Caso voc\u00ea n\u00e3o saiba o que s\u00e3o, deixamos esta p\u00e1gina onde \u00e9 explicado <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/identidades-produtos-igualdades-notaveis-exercicios-resolvidos\/\">quais s\u00e3o os produtos not\u00e1veis<\/a><\/span><\/strong> , como s\u00e3o calculados e para que servem. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-diferencia-de-cubos\"><\/span> Diferen\u00e7a de f\u00f3rmula de cubos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dada a defini\u00e7\u00e3o de diferen\u00e7a ou subtra\u00e7\u00e3o de cubos, veremos qual \u00e9 a f\u00f3rmula para este tipo de igualdade not\u00e1vel: <\/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-la-difference-ou-la-soustraction-de-cubes.png\" alt=\"f\u00f3rmula para diferen\u00e7a ou subtra\u00e7\u00e3o de cubos\" class=\"wp-image-2731\" width=\"304\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Portanto, subtrair dois termos do cubo \u00e9 igual \u00e0 diferen\u00e7a desses dois termos multiplicada pelo quadrado do primeiro termo, mais o produto das duas quantidades, mais o quadrado do segundo termo.<\/p>\n<p> Portanto, quando aplicamos a f\u00f3rmula da diferen\u00e7a de cubos, <a href=\"https:\/\/mathority.org\/pt\"><strong><span style=\"text-decoration: underline;\">estamos na verdade fatorando um polin\u00f4mio de grau 3<\/span><\/strong><\/a> , porque estamos transformando um polin\u00f4mio em um produto de dois fatores. Clique no link acima para saber mais sobre fatora\u00e7\u00e3o de polin\u00f4mios.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-diferencias-de-cubos\"><\/span> Exemplos de diferen\u00e7a de cubo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o do conceito de diferen\u00e7a de cubos perfeitos, veremos v\u00e1rios exemplos de fatora\u00e7\u00e3o da subtra\u00e7\u00e3o de cubos utilizando sua f\u00f3rmula:<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<ul>\n<li> Fatore a seguinte diferen\u00e7a 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-909f0f47fc67c8ad20d18d0f7afbe37c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3-8\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Na verdade, \u00e9 uma diferen\u00e7a 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-77dbc9d52cba4a6adfcc9c5d6b7c5080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3-8=x^3-2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Podemos, portanto, usar a f\u00f3rmula da diferen\u00e7a de cubos perfeitos 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-52d5ddbcfea3f7d3d492b8f0ead32dc2_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-24074f74c6a536c91c3e9265e1b7ec30_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 agora s\u00f3 nos resta fazer 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-01983c298ec4dfadaad4c6b45855090f_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> A partir da express\u00e3o obtida, podemos facilmente determinar que<\/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-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 uma raiz do polin\u00f4mio. \u00c9 importante entender completamente esse conceito, ent\u00e3o se voc\u00ea n\u00e3o tiver total clareza sobre isso, recomendo ver <a href=\"https:\/\/mathority.org\/pt\/raizes-de-um-polinomio\/\"><strong><span style=\"text-decoration: underline;\">como tirar a raiz de um polin\u00f4mio<\/span><\/strong><\/a> .<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<ul>\n<li> Fatore o seguinte bin\u00f4mio negativo usando a f\u00f3rmula de subtra\u00e7\u00e3o de cubo perfeito.<\/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-a8d67849a4b6896846812ddca928092f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> O bin\u00f4mio deste problema tamb\u00e9m \u00e9 uma diferen\u00e7a de cubos, pois 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-534b566d3a3b0943a22cdb5220132623_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, aplicar a f\u00f3rmula de subtra\u00e7\u00e3o de cubos perfeitos para simplificar a express\u00e3o polinomial:<\/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-52d5ddbcfea3f7d3d492b8f0ead32dc2_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-9d9d52829d37cbca4716887d7c319ed4_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> E, por fim, s\u00f3 nos resta 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-4c4041ac5fdf0fcccec106c4e5a957a0_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> Embora pare\u00e7am conceitos semelhantes, a diferen\u00e7a de cubos n\u00e3o deve ser confundida com um bin\u00f4mio c\u00fabico, pois este \u00faltimo \u00e9 uma identidade diferente (e mais importante). Deixamos este link para que voc\u00ea possa ver o que \u00e9 a <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/binomio-ao-cubo\/\">f\u00f3rmula binomial ao cubo<\/a><\/span><\/strong> e quais s\u00e3o as diferen\u00e7as entre essas duas identidades not\u00e1veis. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-diferencia-de-cubos\"><\/span> Problemas resolvidos de diferen\u00e7a de cubo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea entenda perfeitamente como resolver uma diferen\u00e7a de cubos, preparamos diversos exerc\u00edcios resolvidos passo a passo. N\u00e3o se esque\u00e7a de que voc\u00ea pode nos fazer qualquer pergunta na se\u00e7\u00e3o de coment\u00e1rios (abaixo).\u2b07\u2b07<\/p>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Fatore a seguinte diferen\u00e7a de cubos usando 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-d2087daeacab49fe1a03a67113c1a7cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^6-27x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"74\" 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\"> A express\u00e3o corresponde a uma diferen\u00e7a 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-4563571bc34b85f3aca39d2a44a929ee_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 diferen\u00e7a de cubos perfeitos para fatorar a express\u00e3o c\u00fabica em uma multiplica\u00e7\u00e3o de um bin\u00f4mio por 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-52d5ddbcfea3f7d3d492b8f0ead32dc2_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-f9fd889ba4827922378d85989d97fedc_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 e assim encontramos 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-0a4b6341424951063b66e5ae4d7f20eb_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 diferen\u00e7a 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-d46d0e5b09ae81b6e7381832fa957a2a_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-233d8f9883af759cbdc82da52eb8d49c_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-5917ade9de4939b40e2b94372a5df4b1_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 diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos perfeitos, portanto \u00e9 suficiente resolver as multiplica\u00e7\u00f5es de 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-34e5fe437cf5dfaa305bbbcd8927b2c0_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=\"90\" 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-8af23875bcc05db2a69c8bf1e263274b_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=\"90\" 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-394ede96d4736d84a33ef9029ade5a90_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> \ud83d\udc49\ud83d\udc49\ud83d\udc49 Por fim, voc\u00ea tamb\u00e9m pode estar interessado em saber como calcular uma <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/diferenca-ou-subtracao-de-quadrados\/\">subtra\u00e7\u00e3o de quadrados<\/a><\/span><\/strong> . Esta \u00e9 outra identidade not\u00e1vel semelhante \u00e0 que acabamos de ver (mas \u00e9 muito mais usada). Descubra quais s\u00e3o as diferen\u00e7as entre essas duas identidades not\u00e1veis clicando no link.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina explicamos como fatorar uma diferen\u00e7a de cubos (f\u00f3rmula). Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos e at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. Qual \u00e9 a diferen\u00e7a entre cubos? Em matem\u00e1tica, a diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos \u00e9 um bin\u00f4mio (polin\u00f4mio com apenas dois mon\u00f4mios) composto por um termo positivo e um &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/subtracao-de-diferenca-de-cubos\/\"> <span class=\"screen-reader-text\">Diferen\u00e7a (ou subtra\u00e7\u00e3o) de 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-341","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>Diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos - 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\/subtracao-de-diferenca-de-cubos\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina explicamos como fatorar uma diferen\u00e7a de cubos (f\u00f3rmula). 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