{"id":52,"date":"2023-09-17T07:29:56","date_gmt":"2023-09-17T07:29:56","guid":{"rendered":"https:\/\/mathority.org\/de\/algebraische-multiplikation-von-monomen-multiplikation-von-beispielen-und-gelosten-ubungen\/"},"modified":"2023-09-17T07:29:56","modified_gmt":"2023-09-17T07:29:56","slug":"algebraische-multiplikation-von-monomen-multiplikation-von-beispielen-und-gelosten-ubungen","status":"publish","type":"post","link":"https:\/\/mathority.org\/de\/algebraische-multiplikation-von-monomen-multiplikation-von-beispielen-und-gelosten-ubungen\/","title":{"rendered":"Algebraische multiplikation von monomen"},"content":{"rendered":"<p>Hier erfahren Sie, was Monommultiplikation ist und wie man sie durchf\u00fchrt. Dar\u00fcber hinaus k\u00f6nnen Sie Beispiele f\u00fcr die Multiplikation von Monomen sehen und sogar mit \u00dcbungen \u00fcben, die Schritt f\u00fcr Schritt gel\u00f6st werden. Und schlie\u00dflich erkl\u00e4ren wir die Eigenschaften des Produkts von Monomen.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-multiplicar-monomios\"><\/span>So multiplizieren Sie Monome<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um zu verstehen, wie man eine Multiplikation von Monomen l\u00f6st, muss man nat\u00fcrlich zun\u00e4chst wissen, was Monome sind. Wir empfehlen Ihnen daher, einen Blick auf die <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/de\/monome\/\">Erkl\u00e4rung der Monome<\/a><\/span><\/strong> zu werfen, bevor Sie fortfahren.<\/p>\n<p> Dann erfolgt die Multiplikation von Monomen wie folgt:<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> In der Mathematik ist das Ergebnis der <strong>Multiplikation zweier Monome<\/strong> ein weiteres Monom, dessen Koeffizient das Produkt der Koeffizienten der Monome ist und dessen Literalteil durch Multiplikation der Variablen mit derselben Basis, also durch Addition ihrer Exponenten, erhalten wird. <\/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=\"Multiplikation von Monomen mit Exponenten\" class=\"wp-image-203\" width=\"194\" height=\"196\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Um zwei verschiedene Monome zu multiplizieren, m\u00fcssen wir daher die Koeffizienten zwischen ihnen multiplizieren und die Exponenten der Potenzen mit derselben Basis addieren.<\/p>\n<p> <strong>Wenn wir jedoch zwei Monome mit unterschiedlichen Basispotenzen multiplizieren<\/strong> , m\u00fcssen wir einfach ihre Koeffizienten miteinander multiplizieren und die Potenzen gleich lassen. Zum Beispiel:<\/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> Schlie\u00dflich muss daran erinnert werden, dass die <strong>Zeichenregel (oder das Gesetz)<\/strong> nat\u00fcrlich auch f\u00fcr das Produkt der Koeffizienten von Monomen gilt, da die Multiplikation eine arithmetische Operation ist. ALSO:<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Ein positives Monom multipliziert mit einem anderen positiven Monom ergibt ein positives Monom:<\/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;\">Ein positives Monom multipliziert mit einem negativen Monom (oder umgekehrt) ist \u00e4quivalent zu einem negativen Monom:<\/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;\">Zwei negative Monome miteinander multipliziert ergeben ein positives Monom:<\/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> Andererseits ist zu beachten, dass das Verfahren zur <a href=\"https:\/\/mathority.org\/de\/division-von-monomen,-division-von-beispielen-und-gelosten-ubungen\/\"><strong><span style=\"text-decoration: underline;\">Division von Monomen<\/span><\/strong><\/a> anders durchgef\u00fchrt wird, tats\u00e4chlich ist es viel komplizierter. Aus diesem Grund empfehlen wir Ihnen, diese verlinkte Seite zu besuchen, auf der wir Ihnen erkl\u00e4ren, wie zwei oder mehr Monome geteilt werden. Dar\u00fcber hinaus k\u00f6nnen Sie Beispiele sehen und mit Schritt f\u00fcr Schritt gel\u00f6sten \u00dcbungen \u00fcben. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-multiplicaciones-de-monomios\"><\/span> Beispiele f\u00fcr Monommultiplikationen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Damit Sie klar verstehen, wie Monome multipliziert werden, zeigen wir Ihnen im Folgenden einige Beispiele f\u00fcr die Multiplikation zwischen Monomen: <\/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> Aufgaben zur Multiplikation von Monomen gel\u00f6st<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nachfolgend finden Sie einige Schritt-f\u00fcr-Schritt-\u00dcbungen zum Multiplizieren von Monomen, damit Sie mehr \u00fcben k\u00f6nnen:<\/p>\n<h3 class=\"wp-block-heading\"> \u00dcbung 1<\/h3>\n<p> Berechnen Sie die folgenden Multiplikationen von Monomen: <\/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>Sehen Sie sich die L\u00f6sung an<\/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\">\u00dcbung 2<\/h3>\n<p> L\u00f6sen Sie die folgenden Multiplikationen von Monomen: <\/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>Sehen Sie sich die L\u00f6sung an<\/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\">\u00dcbung 3<\/h3>\n<p> Vereinfachen Sie die folgenden Multiplikationen von Monomen so weit wie m\u00f6glich: <\/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>Sehen Sie sich die L\u00f6sung an<\/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}&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220;><\/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> Eigenschaften der Monommultiplikation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Das Produkt von Monomen hat folgende Eigenschaften:<\/p>\n<ul>\n<li> <strong>Kommutative Eigenschaft<\/strong> : Die Reihenfolge der multiplizierenden Monome ver\u00e4ndert das Ergebnis der Multiplikation nicht.<\/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>Assoziative Eigenschaft<\/strong> : Wenn drei oder mehr Monome multipliziert werden, ist das Produktergebnis dasselbe, unabh\u00e4ngig davon, wie die Faktoren gruppiert sind:<\/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>Verteilungseigenschaft<\/strong> : Die Summe zweier Monome multipliziert mit einem Drittel ist gleich der Summe jeder Addition multipliziert mit dem dritten Monom. <\/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>Hier erfahren Sie, was Monommultiplikation ist und wie man sie durchf\u00fchrt. Dar\u00fcber hinaus k\u00f6nnen Sie Beispiele f\u00fcr die Multiplikation von Monomen sehen und sogar mit \u00dcbungen \u00fcben, die Schritt f\u00fcr Schritt gel\u00f6st werden. Und schlie\u00dflich erkl\u00e4ren wir die Eigenschaften des Produkts von Monomen. So multiplizieren Sie Monome Um zu verstehen, wie man eine Multiplikation von &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/de\/algebraische-multiplikation-von-monomen-multiplikation-von-beispielen-und-gelosten-ubungen\/\"> <span class=\"screen-reader-text\">Algebraische multiplikation von monomen<\/span> Weiterlesen &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":[13],"tags":[],"class_list":["post-52","post","type-post","status-publish","format-standard","hentry","category-monome"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Wie werden Monome multipliziert? 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