{"id":50,"date":"2023-09-17T07:29:56","date_gmt":"2023-09-17T07:29:56","guid":{"rendered":"https:\/\/mathority.org\/pt\/multiplicacao-algebrica-de-monomas-multiplicacao-de-exemplos-e-exercicios-resolvidos\/"},"modified":"2023-09-17T07:29:56","modified_gmt":"2023-09-17T07:29:56","slug":"multiplicacao-algebrica-de-monomas-multiplicacao-de-exemplos-e-exercicios-resolvidos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/multiplicacao-algebrica-de-monomas-multiplicacao-de-exemplos-e-exercicios-resolvidos\/","title":{"rendered":"Multiplica\u00e7\u00e3o alg\u00e9brica de mon\u00f4mios"},"content":{"rendered":"<p>Aqui voc\u00ea descobrir\u00e1 o que \u00e9 multiplica\u00e7\u00e3o monomial e como faz\u00ea-la. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de multiplica\u00e7\u00e3o de mon\u00f4mios e at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. E finalmente, explicamos as propriedades do produto de mon\u00f4mios.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-multiplicar-monomios\"><\/span>Como multiplicar mon\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Obviamente, para entender como resolver uma multiplica\u00e7\u00e3o de mon\u00f4mios, primeiro voc\u00ea precisa saber o que s\u00e3o mon\u00f4mios. Portanto, recomendamos que voc\u00ea d\u00ea uma olhada na <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/monomas\/\">explica\u00e7\u00e3o dos mon\u00f4mios<\/a><\/span><\/strong> antes de continuar.<\/p>\n<p> Ent\u00e3o, a multiplica\u00e7\u00e3o dos mon\u00f4mios \u00e9 feita da seguinte forma:<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Em matem\u00e1tica, o resultado da <strong>multiplica\u00e7\u00e3o de dois mon\u00f4mios<\/strong> \u00e9 outro mon\u00f4mio cujo coeficiente \u00e9 o produto dos coeficientes dos mon\u00f4mios e cuja parte literal \u00e9 obtida multiplicando as vari\u00e1veis que t\u00eam a mesma base, ou seja, somando seus expoentes. <\/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\/multiplication-de-monomes-1.png\" alt=\"multiplica\u00e7\u00e3o de mon\u00f4mios com expoentes\" class=\"wp-image-203\" width=\"194\" height=\"196\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Portanto, para multiplicar dois mon\u00f4mios diferentes, devemos multiplicar os coeficientes entre eles e somar os expoentes das pot\u00eancias que possuem a mesma base.<\/p>\n<p> No entanto, <strong>se multiplicarmos dois mon\u00f4mios com pot\u00eancias de base diferentes<\/strong> , precisamos simplesmente multiplicar seus coeficientes e deixar as pot\u00eancias iguais. Por 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-91a6b9c012d06d618d61f97a1648fc3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x^2\\cdot 3y^4 = (5\\cdot 3) x^2y^4 = 15x^2y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por fim, \u00e9 preciso lembrar que, obviamente, a <strong>regra (ou lei) dos sinais<\/strong> tamb\u00e9m se aplica ao produto dos coeficientes dos mon\u00f4mios, pois a multiplica\u00e7\u00e3o consiste em uma opera\u00e7\u00e3o aritm\u00e9tica. ENT\u00c3O:<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Um mon\u00f4mio positivo multiplicado por outro mon\u00f4mio positivo \u00e9 igual a um mon\u00f4mio positivo:<\/span><\/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-2e2a155d86c571f8b9207dd30dfc03a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^6\\cdot 4x^3 = 8x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">Um mon\u00f4mio positivo multiplicado por um mon\u00f4mio negativo (ou vice-versa) \u00e9 equivalente a um mon\u00f4mio negativo:<\/span> <\/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-e635dfc7bb40f6a27f1388dd863e57a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x^6\\cdot 4x^3 = -8x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"143\" 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-532ca30b6ce7087107b23026d56113bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^6\\cdot (-4x^3) = -8x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"157\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Dois mon\u00f4mios negativos multiplicados d\u00e3o um mon\u00f4mio positivo:<\/span><\/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-61211090ded1d43cbbacca6e99cc68d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x^6\\cdot (-4x^3) = 8x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por outro lado, deve-se destacar que o procedimento de <a href=\"https:\/\/mathority.org\/pt\/divisao-de-monomas-dividir-exemplos-e-exercicios-resolvidos\/\"><strong><span style=\"text-decoration: underline;\">divis\u00e3o de mon\u00f4mios<\/span><\/strong><\/a> \u00e9 feito de forma diferente, na verdade \u00e9 muito mais complicado. Por isso recomendamos que voc\u00ea visite esta p\u00e1gina vinculada onde explicamos como se dividem dois ou mais mon\u00f4mios e, al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e praticar com exerc\u00edcios resolvidos passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-multiplicaciones-de-monomios\"><\/span> Exemplos de multiplica\u00e7\u00f5es monomiais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea possa entender claramente como os mon\u00f4mios s\u00e3o multiplicados, deixamos abaixo v\u00e1rios exemplos de multiplica\u00e7\u00e3o entre mon\u00f4mios: <\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c373ccffc9ccd101ba2ce02e99abf7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^4 \\cdot 7x^5= (6\\cdot 7)x^{4+5} = 42x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ca04a0873a835eb55f0b7c34208302d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4y \\cdot 2y^3 = (4\\cdot 2)y^{1+3} = 8 y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d47775082b2bf643cd6277a4e74b5b08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x^2y^4\\cdot (-8x^8y^2)=(5\\cdot (-8))x^{2+8}y^{4+2} = -40x^{10}y^6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"390\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2eac10c8abaa8979578beaf8274bd93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x^6y^4 \\cdot (-4x^2z)= (-3\\cdot (-4)) x^{6+2}y^4z= 12x^8y^4z\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"389\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca7602e907500c26d357e713da3bde13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x^8\\cdot 4x^5\\cdot (-x^2) =-12x^{13}\\cdot (-x^2)= 12x^{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"341\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-la-multiplicacion-de-monomios\"><\/span> Exerc\u00edcios resolvidos sobre multiplica\u00e7\u00e3o de mon\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Abaixo est\u00e3o v\u00e1rios exerc\u00edcios passo a passo sobre multiplica\u00e7\u00e3o de mon\u00f4mios para que voc\u00ea possa praticar mais:<\/p>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Calcule as seguintes multiplica\u00e7\u00f5es de mon\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-8b2966b66c4b16041122e639142e7bcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 3x^4\\cdot x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"83\" 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-da823cb11d28cc8c5150d9c82bede60c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 2y^8\\cdot (-5y^6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" 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-66dcbde9536c1464bdeacbfe4d066c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 5x^7\\cdot 6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" 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-3a23c0a17fcd36ffcc9ea8e51fff493f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ -4a^3 \\cdot (-2a)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"132\" 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 a solu\u00e7\u00e3o<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20efcf3552dfa730574118a72f936ef4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 3x^4\\cdot x^5 = (3\\cdot 1)x^{4+5} = \\bm{3x^9}\" 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-9df50340278ae741ac52f48a38ee5200_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 2y^8\\cdot (-5y^6)= (2\\cdot (-5))y^{8+6} = \\bm{-10y^{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"326\" 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-b78b12508f9cae31f2c9629d54b02a04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 5x^7\\cdot 6x^2=(5\\cdot 6)x^{7+2} = \\bm{30x^9}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"254\" 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-7e76e2eccf1ce05294c39055383a22d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ -4a^3 \\cdot (-2a) =(-4\\cdot (-2))a^{3+1} = \\bm{8a^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"325\" style=\"vertical-align: -5px;\"><\/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 as seguintes multiplica\u00e7\u00f5es de mon\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-a13941526446de65e5188475b0ea7de0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 2x^3\\cdot 4x \\cdot (-3x^6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" 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-4a9f455c93714598e9674a632e1d9062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -5x^6\\cdot (-x^3) \\cdot  (-9x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" 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-db69563517fc85e08af5030b411f9114_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 3b^2 \\cdot (-3b^2) \\cdot 6 b^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" 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-a3dfaef0272445d282e740813afdfd89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 7x^3 \\cdot 3x^2 \\cdot 2x^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"131\" 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 a solu\u00e7\u00e3o<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8e74576a123474efdcc8c91a9790d82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 2x^3\\cdot 4x \\cdot (-3x^6) = 8x^4\\cdot (-3x^6) = \\bm{-24x^{10}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"349\" 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-a6317863f115d6e3bba5f4ecf03bedfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -5x^6\\cdot (-x^3) \\cdot  (-9x^4)=5x^9\\cdot (-9x^4) =\\bm{-45x^{13}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"396\" 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-743a7d411fcb347e96683bd7b1c277e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 3b^2 \\cdot (-3b^2) \\cdot 6 b^4=-9b^4\\cdot 6 b^4 =\\bm{ -54b^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"320\" 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-1a9d640c1629c5047c54dfd81875d6ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 7x^3 \\cdot 3x^2 \\cdot 2x^7 = 21x^5\\cdot 2x^7 = \\bm{42x^{12}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"296\" style=\"vertical-align: -5px;\"><\/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> Simplifique ao m\u00e1ximo as seguintes multiplica\u00e7\u00f5es de mon\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-da45476eeb19e88b8c1e10bdce19a65e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 8x^3y^2 \\cdot 5x^4y^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"126\" 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-aa74b10e67a2c8a272a1c9efe8323560_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -6x^5y^2z \\cdot (-4x^4y^9z^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" 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-6d0744f268ff87f0416482d8c8a7caba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -4a^3b^8 \\cdot 5 a^3c^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" 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-a87d7315d5e94a3c11b44e35267ae65c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\  7x^3y^2 \\cdot 5x^8z^4 \\cdot (-2x^2y^5z^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"226\" 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 a solu\u00e7\u00e3o<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-135a047a3847098b675fa240084f7ec9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 8x^3y^2 \\cdot 5x^4y^7 = \\bm{40x^7y^9}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-b3c4c0eb52606eee450b7346121722ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -6x^5y^2z \\cdot (-4x^4y^9z^2) = \\bm{24x^9y^{11}z^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"300\" 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-8b0dbaaa22c70cb0b04ec69ac8cdd901_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -4a^3b^8 \\cdot 5 a^3c^2 = \\bm{-20a^6b^8c^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"245\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 131px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4810644ac307c976e9fba621612325e_l3.png\" height=\"131\" width=\"865\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\text{D)} \\  7x^3y^2 \\cdot 5x^8z^4 \\cdot (-2x^2y^5z^3)= <span class=&quot;ql-right-eqno&quot;>   <\/span><span class=&quot;ql-left-eqno&quot;>   <\/span><img src=&quot;https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bb20ebb96e0dff759d07813f6fff9470_l3.png&quot; height=&quot;22&quot; width=&quot;195&quot; class=&quot;ql-img-displayed-equation quicklatex-auto-format&quot; alt=&quot;\\[35x^{11}y^2z^4\\cdot (-2x^2y^5z^3) =\\]&quot; title=&quot;Rendered by QuickLaTeX.com&quot;\/> \\bm{-70x^{13}y^7z^7}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221;><\/p>\n<\/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=\"Propiedades-de-la-multiplicacion-de-monomios\"><\/span> Propriedades da multiplica\u00e7\u00e3o monomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O produto de mon\u00f4mios possui as seguintes propriedades:<\/p>\n<ul>\n<li> <strong>Propriedade comutativa<\/strong> : a ordem dos mon\u00f4mios multiplicadores n\u00e3o modifica o resultado da multiplica\u00e7\u00e3o.<\/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-cbf793ba721782e5f755715ee11ca3b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x^5 \\cdot 2x^4 = 6x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" 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-184241d9ec2c69af48f36f6700db959a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^4 \\cdot 3x^5 = 6x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Propriedade associativa<\/strong> : Quando tr\u00eas ou mais mon\u00f4mios s\u00e3o multiplicados, o resultado do produto \u00e9 o mesmo independente de como os fatores est\u00e3o agrupados:<\/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-39e6c05df0f9938aa2bf63ede33299d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x \\cdot 4x^2) \\cdot 3x^5 = 24x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"169\" 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-755e055722ef8c0fe45dc0b1a6c3526e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x \\cdot (4x^2 \\cdot 3x^5) = 24x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Propriedade distributiva<\/strong> : a soma de dois mon\u00f4mios multiplicada por um ter\u00e7o \u00e9 igual \u00e0 soma de cada adi\u00e7\u00e3o multiplicada pelo terceiro mon\u00f4mio. <\/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-b68365005bee1dbe3e518e9842cd66a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x^6 \\cdot (3x^4+5x^4) = 4x^6 \\cdot 3x^4 + 4x^6 \\cdot 5x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"305\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Aqui voc\u00ea descobrir\u00e1 o que \u00e9 multiplica\u00e7\u00e3o monomial e como faz\u00ea-la. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de multiplica\u00e7\u00e3o de mon\u00f4mios e at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. E finalmente, explicamos as propriedades do produto de mon\u00f4mios. Como multiplicar mon\u00f4mios Obviamente, para entender como resolver uma multiplica\u00e7\u00e3o de mon\u00f4mios, primeiro voc\u00ea precisa saber &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/multiplicacao-algebrica-de-monomas-multiplicacao-de-exemplos-e-exercicios-resolvidos\/\"> <span class=\"screen-reader-text\">Multiplica\u00e7\u00e3o alg\u00e9brica de mon\u00f4mios<\/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":[18],"tags":[],"class_list":["post-50","post","type-post","status-publish","format-standard","hentry","category-monomios"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Como os mon\u00f4mios s\u00e3o multiplicados? 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