{"id":331,"date":"2023-07-06T06:31:47","date_gmt":"2023-07-06T06:31:47","guid":{"rendered":"https:\/\/mathority.org\/pt\/binomio-ao-cubo\/"},"modified":"2023-07-06T06:31:47","modified_gmt":"2023-07-06T06:31:47","slug":"binomio-ao-cubo","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/binomio-ao-cubo\/","title":{"rendered":"Cubo binomial"},"content":{"rendered":"<p>Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o da resolu\u00e7\u00e3o do produto not\u00e1vel de um bin\u00f4mio ao cubo (f\u00f3rmula), seja (a+b) <sup>3<\/sup> ou (ab) <sup>3<\/sup> . Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e exerc\u00edcios resolvidos passo a passo desde bin\u00f4mios at\u00e9 o cubo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-binomio-al-cubo\"><\/span> O que \u00e9 um bin\u00f4mio ao cubo?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um <strong>bin\u00f4mio ao cubo<\/strong> \u00e9 um polin\u00f4mio composto por dois termos elevado a 3. Consequentemente, a express\u00e3o alg\u00e9brica de um bin\u00f4mio ao cubo pode ser <strong>(a+b) <sup>3<\/sup><\/strong> ou <strong>(ab) <sup>3<\/sup><\/strong> , dependendo se adicionamos ou subtra\u00edmos seus mon\u00f4mios.<\/p>\n<p> Al\u00e9m disso, o bin\u00f4mio ao cubo \u00e9 uma das identidades not\u00e1veis (ou produtos not\u00e1veis). Mais precisamente, corresponde a uma das <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/identidades-produtos-igualdades-notaveis-exercicios-resolvidos\/\">identidades not\u00e1veis do cubo<\/a><\/span><\/strong> (ou c\u00fabico). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-al-cubo\"><\/span> f\u00f3rmula do cubo binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Como vimos na defini\u00e7\u00e3o de bin\u00f4mio ao cubo, esse tipo de identidade not\u00e1vel pode consistir em adi\u00e7\u00e3o ou subtra\u00e7\u00e3o. Portanto, a f\u00f3rmula varia um pouco dependendo se \u00e9 um bin\u00f4mio positivo ou um bin\u00f4mio negativo e, portanto, veremos cada caso separadamente.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cubo-de-una-suma\"><\/span> cubo de uma soma<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Quando uma soma \u00e9 elevada ao cubo, podemos calcul\u00e1-la usando a f\u00f3rmula do cubo de uma 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\/binome-dune-somme-ou-somme-au-cube-formule.png\" alt=\"bin\u00f4mio de uma f\u00f3rmula de soma ao cubo\" class=\"wp-image-2810\" width=\"286\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> De modo que um bin\u00f4mio ao cubo (adi\u00e7\u00e3o) \u00e9 igual ao cubo do primeiro, mais o triplo do quadrado do primeiro vezes o segundo, mais o triplo do primeiro vezes o quadrado do segundo, mais o cubo do segundo.<\/p>\n<p> Outro m\u00e9todo para calcular o cubo de um bin\u00f4mio \u00e9 o bin\u00f4mio de Newton (ou teorema binomial). Deixamos o seguinte link com a explica\u00e7\u00e3o deste teorema porque \u00e9 muito \u00fatil conhecer esta f\u00f3rmula, pois funciona n\u00e3o s\u00f3 para pot\u00eancias de bin\u00f4mios de terceiro grau, mas tamb\u00e9m para expoentes superiores. Ent\u00e3o clique neste link para conhecer e poder praticar com <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/formula-do-teorema-binomial-ou-binomial-de-newton-e-exercicios-resolvidos\/\">exerc\u00edcios binomiais de Newton resolvidos<\/a><\/span><\/strong> .<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cubo-de-una-diferencia\"><\/span> cubo de uma diferen\u00e7a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Por outro lado, se em vez de uma soma tivermos uma diferen\u00e7a (ou subtra\u00e7\u00e3o) elevada ao cubo, a f\u00f3rmula do bin\u00f4mio ao cubo muda no sinal dos termos pares: <\/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-de-difference-de-la-formule-du-cube.png\" alt=\"bin\u00f4mio de uma diferen\u00e7a ou subtra\u00e7\u00e3o \u00e0 f\u00f3rmula do cubo\" class=\"wp-image-2811\" width=\"286\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Portanto, um bin\u00f4mio ao cubo (subtra\u00e7\u00e3o) \u00e9 igual ao cubo do primeiro, menos tr\u00eas vezes o quadrado do primeiro pelo segundo, mais tr\u00eas vezes o primeiro ao quadrado do segundo, menos o cubo do segundo.<\/p>\n<p> Assim, a \u00fanica diferen\u00e7a entre as f\u00f3rmulas do cubo de uma soma e do cubo de uma diferen\u00e7a \u00e9 nos sinais do segundo e do quarto termos, pois no bin\u00f4mio de uma soma todos s\u00e3o positivos e, ao contr\u00e1rio, em os bin\u00f4mios de uma subtra\u00e7\u00e3o s\u00e3o ambos negativos.<\/p>\n<p> Acabamos de ver o que s\u00e3o o bin\u00f4mio de soma e o bin\u00f4mio de diferen\u00e7a. Pois bem, voc\u00ea deve saber que a <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/formula-para-o-produto-da-soma-pela-diferenca\/\">soma por diferen\u00e7a<\/a><\/span><\/strong> de dois bin\u00f4mios tamb\u00e9m \u00e9 uma identidade not\u00e1vel e, de fato, faz parte do top 3 (o mais importante). Voc\u00ea pode ver qual \u00e9 a f\u00f3rmula para uma soma vezes uma diferen\u00e7a e como ela \u00e9 aplicada na p\u00e1gina vinculada. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-binomios-al-cubo\"><\/span> Exemplos de bin\u00f4mios c\u00fabicos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a f\u00f3rmula do cubo de uma soma e a f\u00f3rmula do cubo de uma diferen\u00e7a, veremos um exemplo de resolu\u00e7\u00e3o de cada tipo de bin\u00f4mio ao cubo para finalizar a compreens\u00e3o do conceito. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-cubo-de-una-suma\"><\/span> Exemplo do cubo de uma soma<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Resolva o bin\u00f4mio para o seguinte cubo 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-9b6665bb45814802bf3d7dbb8b68c771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Neste problema, temos um bin\u00f4mio cujos dois termos s\u00e3o positivos. Devemos, portanto, aplicar a f\u00f3rmula para uma soma ao cubo:<\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora precisamos encontrar 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> 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> corresponde \u00e0 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> \u00e9 o n\u00famero 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-909b3b4a2f976c165f160a6765b3ed9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a+b)^3\\\\[2ex] (x+2)^3 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x \\\\[2ex] b=2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Portanto, calculamos o bin\u00f4mio ao cubo substituindo 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> 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\/exemple-dun-binome-somme-et-difference-au-cube.jpg\" alt=\"exemplo de um bin\u00f4mio ao cubo de soma e diferen\u00e7a\" class=\"wp-image-2468\" width=\"419\" height=\"168\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-cubo-de-una-diferencia\"><\/span> Exemplo de um cubo de diferen\u00e7a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Calcule o pr\u00f3ximo bin\u00f4mio ao cubo (diferen\u00e7a) usando sua f\u00f3rmula correspondente:<\/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-fb0dbc34da8cea6a7d6622c9a3c5faba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3x-2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Neste exerc\u00edcio, temos um par com um elemento positivo e um elemento negativo. Devemos, portanto, usar a f\u00f3rmula para uma diferen\u00e7a ao cubo:<\/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-746a96ec30fac619eedf62054c377fe5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3 = a^3-3a^2b+3ab^2 -b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00c9 portanto necess\u00e1rio identificar o valor 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> representa o mon\u00f4mio 3x 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 o 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-a792ec6dead8466ec6a2cb2a43d9fab4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a-b)^3\\\\[2ex] (3x-2)^3 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=3x \\\\[2ex] b=2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Observe que o par\u00e2metro<\/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-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 simplesmente igual a 2, sem o sinal negativo do n\u00famero. \u00c9 importante ter isso em mente para aplicar corretamente a f\u00f3rmula.<\/p>\n<p> Por fim, resolvemos o bin\u00f4mio ao cubo colocando 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> 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-cube-negatif-parfait.jpg\" alt=\"bin\u00f4mio cubo perfeito negativo\" class=\"wp-image-2476\" width=\"501\" height=\"169\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-binomio-al-cubo\"><\/span> Prova da f\u00f3rmula do cubo binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir, demonstraremos a f\u00f3rmula para um bin\u00f4mio ao cubo. Embora obviamente n\u00e3o seja necess\u00e1rio saber, \u00e9 sempre bom entender a \u00e1lgebra por tr\u00e1s de qualquer f\u00f3rmula.<\/p>\n<p> De um bin\u00f4mio ao cubo positivo:<\/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-380239d5f1b18e11f3b6b0931a4f14d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A express\u00e3o acima pode ser decomposta matematicamente no 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-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> pelo seu 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-d89c1125bf18f5ec3b34a3bc8e4de45b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3=(a+b)\\cdot (a+b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Al\u00e9m disso, a dupla<\/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> elevado a 2 \u00e9 uma identidade not\u00e1vel, portanto, podemos resolv\u00ea-la com a <a href=\"https:\/\/mathority.org\/pt\/quadrado-de-uma-soma-ou-soma-ao-quadrado\/\"><strong><span style=\"text-decoration: underline;\">f\u00f3rmula do quadrado de uma soma<\/span><\/strong><\/a> :<\/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-4b1c6920425dd90a9526a1eaccf056b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)\\cdot (a+b)^2=(a+b)\\cdot (a^2+2ab+b^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"328\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora 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-06771ecbb13542eae2a68477f849d729_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a+b)\\cdot (a^2+2ab+b^2) &amp; = a\\cdot a^2 +a\\cdot 2ab + a\\cdot b^2+b\\cdot a^2 +b\\cdot 2ab +b \\cdot b^2 \\\\[2ex] &amp; = a^3+2a^2b+ab^2+ba^2+2ab^2+b^3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"555\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> E, por fim, s\u00f3 temos que agrupar os termos que se parecem:<\/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-27d0da0e0e3ce760508c47f425fd1d68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+2a^2b+ab^2+ba^2+2ab^2+b^3 = a^3+3a^2b+3ab^2+b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"445\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Para que a f\u00f3rmula de um bin\u00f4mio ao cubo seja verificada:<\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Logicamente, para deduzir a f\u00f3rmula do cubo binomial negativo, siga os mesmos passos que acabamos de fazer, mas come\u00e7ando com o termo<\/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-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> sinal alterado.<\/p>\n<p> Por outro lado, a f\u00f3rmula de um bin\u00f4mio ao cubo tamb\u00e9m pode ser demonstrada usando <a href=\"https:\/\/mathority.org\/pt\/tartaglia-ou-triangulo-de-pascal\/\"><strong><span style=\"text-decoration: underline;\">o tri\u00e2ngulo de Pascal (ou de Tartaglia)<\/span><\/strong><\/a> . Caso voc\u00ea n\u00e3o saiba o que \u00e9 esse truque matem\u00e1tico, deixamos este link onde \u00e9 explicado passo a passo. Al\u00e9m disso, voc\u00ea poder\u00e1 ver todas as aplica\u00e7\u00f5es que possui e a hist\u00f3ria particular deste tri\u00e2ngulo alg\u00e9brico t\u00e3o especial. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-binomios-al-cubo\"><\/span> Problemas resolvidos de cubo binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea possa praticar com a teoria que acabamos de ver sobre o c\u00e1lculo de um bin\u00f4mio elevado \u00e0 pot\u00eancia de 3, preparamos diversos exerc\u00edcios resolvidos passo a passo sobre o bin\u00f4mio ao cubo.<\/p>\n<p> Ent\u00e3o n\u00e3o esque\u00e7a de nos contar o que achou dessa explica\u00e7\u00e3o! E voc\u00ea tamb\u00e9m pode nos tirar qualquer d\u00favida que surgir! \ud83d\udc4d\ud83d\udc4d\ud83d\udc4d<\/p>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Encontre os seguintes bin\u00f4mios ao cubo: <\/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-ca75501df4056045f750323893bee27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x+4)^3\" 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-f1ae5aad30adde91e86d6bb696b6adc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(x^2-5\\right)^3\" 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-debc2fbed1f43204a1d3b191ce697175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(2x-1\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" 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-641ad931932e2d32742c712339a76903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (5x+2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"97\" 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 binomial ao cubo, dependendo se \u00e9 uma adi\u00e7\u00e3o ou uma subtra\u00e7\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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-5a9a96bd2d1f115178fbbcf19c8047c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3 = a^3-3a^2b+3ab^2-b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-14695fb807e2df89352fdd1c1dced2ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}(x+4)^3&amp; =x^3+3\\cdot x^2\\cdot 4 +3\\cdot x\\cdot 4^2+4^3\\\\[2ex] &amp; =x^3+3\\cdot x^2\\cdot 4 +3\\cdot x\\cdot 16+64 \\\\[2ex] &amp; = \\bm{x^3+12x^2+48x+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"342\" 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-5be0d584351feb0bef5572ca5c9e159a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(x^2-5\\right)^3&amp; =\\left(x^2\\right)^3-3\\cdot \\left(x^2\\right)^2\\cdot 5 +3\\cdot x^2\\cdot 5^2-5^3\\\\[2ex] &amp; =x^6-3\\cdot x^4\\cdot 5 +3\\cdot x^2\\cdot 25-125 \\\\[2ex] &amp; = \\bm{x^6-15x^4+75x^2-125}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"404\" 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-f44f9c3283dad97321644c6e559f64ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned}\\left(2x-1\\right)^3&amp; =\\left(2x\\right)^3-3\\cdot \\left(2x\\right)^2\\cdot 1 +3\\cdot 2x\\cdot 1^2-1^3\\\\[2ex] &amp; =8x^3-3\\cdot 4x^2\\cdot 1 +3\\cdot 2x\\cdot 1-1 \\\\[2ex] &amp; = \\bm{8x^3-12x^2+6x-1}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"401\" 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-156e7619e4d6ef129f04250af8197d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned}(5x+2)^3&amp; =(5x)^3+3\\cdot \\left(5x\\right)^2\\cdot 2 +3\\cdot 5x\\cdot 2^2+2^3\\\\[2ex] &amp; =125x^3+3\\cdot 25x^2\\cdot 2 +3\\cdot 5x\\cdot 4+8 \\\\[2ex] &amp; = \\bm{125x^3+150x^2+60x+8}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"402\" 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 bin\u00f4mios ao cubo de duas quantidades aplicando 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-fa956af1cab818af1f22653b384dfc21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(4x^2-y^5\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"118\" 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-3a6734ab696568f02b53cc593ce70939_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(6x^3+2y^4\\right)^3\" 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-02817aca9c2bc6ddaf621c52a024719d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\left(\\frac{9}{2}x^2-\\frac{4}{3}x\\right)^3\" 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 exerc\u00edcio, voc\u00ea deve usar a f\u00f3rmula para uma soma e uma subtra\u00e7\u00e3o ao cubo: <\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-5a9a96bd2d1f115178fbbcf19c8047c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3 = a^3-3a^2b+3ab^2-b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-386169975ac336c1732a91ebd6d0830c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}\\left(4x^2-y^5\\right)^3&amp; =\\left(4x^2\\right)^3-3\\cdot \\left(4x^2\\right)^2\\cdot y^5 +3\\cdot 4x^2\\cdot \\left(y^5\\right)^2-\\left(y^5\\right)^3\\\\[2ex] &amp; =64x^6-3\\cdot 16x^4\\cdot y^5 +3\\cdot 4x^2\\cdot y^{10}-y^{15} \\\\[2ex] &amp; = \\bm{64x^6-48x^4y^5+12x^2y^{10}-y^{15}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"505\" 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-27c153bf59237b782cc697203d5f235a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(6x^3+2y^4\\right)^3&amp; =\\left(6x^3\\right)^3+3\\cdot \\left(6x^3\\right)^2\\cdot 2y^4 +3\\cdot 6x^3\\cdot \\left(2y^4\\right)^2+\\left(2y^4\\right)^3\\\\[2ex] &amp; =216x^9+3\\cdot 36x^6\\cdot 2y^4 +3\\cdot 6x^3\\cdot 4y^8+8y^{12} \\\\[2ex] &amp; = \\bm{216x^9+216x^6y^4 +72x^3y^8+8y^{12}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"540\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Os mon\u00f4mios do \u00faltimo bin\u00f4mio ao cubo 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-54262e17cdee07e9f36eb92f3b8b5727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\begin{aligned}\\left(\\frac{9}{2}x^2-\\frac{4}{3}x\\right)^3 &amp; =\\left(\\frac{9}{2}x^2\\right)^3-3\\cdot \\left(\\frac{9}{2}x^2\\right)^2\\cdot \\frac{4}{3}x +3\\cdot \\frac{9}{2}x^2\\cdot \\left(\\frac{4}{3}x\\right)^2-\\left(\\frac{4}{3}x\\right)^3\\\\[3ex] &amp; =\\frac{9^3}{2^3}x^6-3\\cdot \\frac{9^2}{2^2}x^4\\cdot \\frac{4}{3}x +3\\cdot \\frac{9}{2}x^2\\cdot \\frac{4^2}{3^2}x^2-\\frac{4^3}{3^3}x^3 \\\\[3ex] &amp;= \\frac{729}{8}x^6-3\\cdot \\frac{81}{4}x^4\\cdot \\frac{4}{3}x +3\\cdot \\frac{9}{2}x^2\\cdot \\frac{16}{9}x^2-\\frac{64}{27}x^3 \\\\[3ex] &amp;= \\frac{729}{8}x^6-3\\cdot \\frac{324}{12}x^5 +3\\cdot \\frac{144}{18}x^4-\\frac{64}{27}x^3 \\\\[3ex] &amp;= \\frac{729}{8}x^6-3\\cdot 27x^5 +3\\cdot 8x^4-\\frac{64}{27}x^3 \\\\[3ex] &amp; = \\mathbf{\\frac{729}{8}}\\bm{x^6-81x^5 +24x^4-}\\mathbf{\\frac{64}{27}}\\bm{x^3}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"375\" width=\"589\" 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 voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o da resolu\u00e7\u00e3o do produto not\u00e1vel de um bin\u00f4mio ao cubo (f\u00f3rmula), seja (a+b) 3 ou (ab) 3 . Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e exerc\u00edcios resolvidos passo a passo desde bin\u00f4mios at\u00e9 o cubo. O que \u00e9 um bin\u00f4mio ao cubo? Um bin\u00f4mio ao cubo \u00e9 um polin\u00f4mio composto &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/binomio-ao-cubo\/\"> <span class=\"screen-reader-text\">Cubo binomial<\/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-331","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>Binomial ao cubo - 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\/binomio-ao-cubo\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binomial ao cubo - Mathority\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o da resolu\u00e7\u00e3o do produto not\u00e1vel de um bin\u00f4mio ao cubo (f\u00f3rmula), seja (a+b) 3 ou (ab) 3 . Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e exerc\u00edcios resolvidos passo a passo desde bin\u00f4mios at\u00e9 o cubo. O que \u00e9 um bin\u00f4mio ao cubo? 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