{"id":96,"date":"2023-09-17T07:27:50","date_gmt":"2023-09-17T07:27:50","guid":{"rendered":"https:\/\/mathority.org\/nl\/operaties-met-monomen-voorbeelden-en-oefeningen-opgelost-1-2-3-4-welke\/"},"modified":"2023-09-17T07:27:50","modified_gmt":"2023-09-17T07:27:50","slug":"operaties-met-monomen-voorbeelden-en-oefeningen-opgelost-1-2-3-4-welke","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/operaties-met-monomen-voorbeelden-en-oefeningen-opgelost-1-2-3-4-welke\/","title":{"rendered":"Operaties met monomials"},"content":{"rendered":"<p>Op deze pagina leggen we uit hoe je alle bewerkingen met monomialen uitvoert (optellen, aftrekken, vermenigvuldigen, delen en macht). Bovendien kunt u voorbeelden zien van elk type operatie met monomials en oefenen met oefeningen die stap voor stap worden opgelost.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Suma-y-resta-de-monomios\"><\/span> Optellen en aftrekken van monomials <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Twee of meer monomialen kunnen alleen worden opgeteld of afgetrokken als het vergelijkbare monomialen zijn, dat wil zeggen als de twee monomialen een identiek letterlijk deel hebben (dezelfde letters en dezelfde exponenten).<\/p>\n<p> Vervolgens is de som (of aftrekking) van twee soortgelijke monomialen gelijk aan een andere monomial die bestaat uit hetzelfde letterlijke deel en de som (of aftrekking) van de co\u00ebffici\u00ebnten van deze twee monomialen. <\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-37\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/somme-de-monomes-exemples.png\" alt=\"wat zijn operaties met monomials\" width=\"200\" height=\"201\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/soustraction-de-monomes-1.png\" alt=\"operaties met monomials 1 die\" class=\"wp-image-151\" width=\"200\" height=\"202\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> Optellen en aftrekken van monomials worden ook respectievelijk optellen en aftrekken van monomials genoemd.<\/p>\n<h3 class=\"wp-block-heading\"> Voorbeelden van optellen en aftrekken van monomials<\/h3>\n<p> Zodat u duidelijk begrijpt hoe u twee of meer monomialen moet optellen en aftrekken, laten we hieronder enkele voorbeelden achter: <\/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-9e5b7ccd3830be06fd2f5165a760b367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x^6+3x^6 = 7x^6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"125\" style=\"vertical-align: -2px;\"><\/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-74bf65eaed8bbd99077260cff7a731dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y^3-2y^3 = 3y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -4px;\"><\/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-3bdda97aea0b54fdbbc1ffb190d88fb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^2y+5x^2y-3x^2y = 4x^2y\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"211\" style=\"vertical-align: -4px;\"><\/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-75b17946f2dc3a4f4f7ec9753107b88d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6abc-7abc+4abc = 3abc\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"202\" style=\"vertical-align: -2px;\"><\/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-60b660491e258b4dbcc9728dfd75d7ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^3y^2-4x^3y+2x^2y^3 = \\color{red} \\bm{\\times}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"228\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<p> De monomialen in het laatste voorbeeld kunnen niet worden opgeteld of afgetrokken omdat ze niet vergelijkbaar zijn of, met andere woorden, verschillende onbekenden of exponenten hebben. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Producto-de-un-numero-por-un-monomio\"><\/span> Product van een aantal maal een monomial <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Om het <strong>product van een monomiaal met een getal op te lossen,<\/strong> vermenigvuldigt u eenvoudigweg de co\u00ebffici\u00ebnt van het monomial met dat getal, waarbij het letterlijke deel van het monomial hetzelfde blijft. <\/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\/produit-ou-multiplication-d-un-nombre-par-un-monome.png\" alt=\"\" class=\"wp-image-393\" width=\"165\" height=\"167\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> Voorbeelden van het vermenigvuldigen van getallen met monomials <\/h3>\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-e92d21eb9de394440a08b38dcbc685d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (6x^3) = (2\\cdot 6)x^3 = 12x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" 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-318cfda7f7d93cc2a20639b21e82fb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-4\\cdot (5x^7) = (-4\\cdot 5)x^7 = -20x^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-7a2dab19c0282d641053ffb115e6bf28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5\\cdot (-3a^4b) = (5\\cdot (-3))a^4b = -15a^4b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"283\" 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-83efc00f783524ec9b40eac2196931f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-7(-6x^9y^5)= (-7\\cdot (-6))x^9y^5=42x^9y^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Multiplicacion-de-monomios\"><\/span> Vermenigvuldiging van monomialen <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Het resultaat van de <strong>vermenigvuldiging van twee monomialen<\/strong> is een andere monomial waarvan de co\u00ebffici\u00ebnt het product is van de co\u00ebffici\u00ebnten van de monomialen en waarvan het letterlijke deel wordt verkregen door de variabelen die dezelfde basis hebben te vermenigvuldigen, dat wil zeggen door hun exponenten op te tellen. <\/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=\"operaties met monomials pdf\" class=\"wp-image-203\" width=\"194\" height=\"196\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Om twee verschillende monomialen te vermenigvuldigen, moeten we daarom de co\u00ebffici\u00ebnten daartussen vermenigvuldigen en de exponenten van de machten met dezelfde basis optellen.<\/p>\n<p> <strong>Als we echter twee monomialen met verschillende basismachten vermenigvuldigen<\/strong> , hoeven we alleen maar hun co\u00ebffici\u00ebnten met elkaar te vermenigvuldigen en de machten hetzelfde te laten. Bijvoorbeeld:<\/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> Aan de andere kant moet bij het vermenigvuldigen van monomialen rekening worden gehouden met de tekenregel:<\/p>\n<ul>\n<li> Een positieve monomial vermenigvuldigd met een positieve monomial levert nog een positieve monomial op.<\/li>\n<li> Een positieve monomial vermenigvuldigd met een negatieve monomial (of omgekeerd) is gelijk aan een negatieve monomial.<\/li>\n<li> Twee negatieve monomialen met elkaar vermenigvuldigd geven aanleiding tot een positieve monomial.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> Voorbeelden van monomiale vermenigvuldigingen<\/h3>\n<p> Hieronder staan verschillende voorbeelden van vermenigvuldiging tussen monomialen, zodat je kunt zien hoe het werkt: <\/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<p> Zoals je hebt gezien, is het oplossen van een vermenigvuldiging van monomialen relatief eenvoudig. Maar u moet er rekening mee houden dat monomialen ook met polynomen kunnen worden vermenigvuldigd, en dat zelfs twee of meer polynomen met elkaar kunnen worden vermenigvuldigd. Als u meer ge\u00efnteresseerd bent, kunt u zien hoe al deze bewerkingen werken door op <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/nl\/vermenigvuldiging-van-polynomen-voorbeelden-oefeningen-opgelost-product-vermenigvuldigen\/\">polynomiale vermenigvuldiging<\/a><\/span><\/strong> te klikken.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-de-monomios\"><\/span> Verdeling van monomialen <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> In de wiskunde is het resultaat van de <strong>deling van monomialen<\/strong> een andere monomial waarvan de co\u00ebffici\u00ebnt gelijk is aan het quoti\u00ebnt van de co\u00ebffici\u00ebnten van de monomialen en waarvan het letterlijke deel wordt verkregen door de variabelen te delen die dezelfde basis hebben, dat wil zeggen door hun exponenten af te trekken. . <\/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\/division-de-monomes-1.png\" alt=\"operaties met monomials 2 welke\" class=\"wp-image-317\" width=\"201\" height=\"202\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Uiteraard kan elke verdeling van monomialen ook als een breuk worden uitgedrukt:<\/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-d022dbe3ddc38f031f0bb5dd4a8a6b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3y^2z : 2x^2y = \\cfrac{8x^3y^2z}{2x^2y} =  4xyz\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"243\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Net als bij vermenigvuldiging is het bij de verdeling van monomialen noodzakelijk om de wet van tekens toe te passen:<\/p>\n<ul>\n<li> Een positieve monomial gedeeld door een positieve monomial geeft nog een positieve monomial.<\/li>\n<li> Een positieve monomial gedeeld door een negatieve monomial (of omgekeerd) is gelijk aan een negatieve monomial.<\/li>\n<li> Twee negatieve monomialen die door elkaar worden gedeeld, geven aanleiding tot een positieve monomial.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> Voorbeelden van de verdeling van monomials<\/h3>\n<p> Hieronder kunt u meer voorbeelden zien van hoe twee of meer monomialen zijn verdeeld: <\/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-0345d3bf8afc735b7e499584142fef76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"7x^6 : 7x^4= (7:7)x^{6-4} = 1x^2=x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"264\" 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-6ba837b0d16f0fe2c78d057c053a72c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12y^5 : 4y^2= (12:4)y^{5-2} = 3y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"237\" 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-99ce1c658885782a0de61d4acaae8f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15x^7y^6 :3x^4y^5= (15:3)x^{7-4}y^{6-5} = 5x^3y\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"318\" 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-344fa60ffc830f331035b6307b698695_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27x^9y^7 :(-3x^5y^2)= (27:(-3))x^{9-5}y^{7-2}= -9x^4y^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"395\" 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-f98903cc9dff2fc60d4baeef41bbce1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-18x^{13} : 3x^4 : (-2x^7) = -6x^9: (-2x^7) = 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"348\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<p> Toen je op een gegeven moment iets nieuws leerde in de wiskunde, vroeg je je vast af: <span style=\"text-decoration: underline;\">waar is het voor<\/span> ? Welnu, monomiale deling wordt gebruikt om polynomen te verdelen. Het is zelfs heel gebruikelijk dat er een fout wordt gemaakt bij het delen van polynomen, omdat twee monomialen verkeerd zijn verdeeld. Daarom raden we aan dat je, nu je bekend bent met de deling tussen monomialen, ziet hoe de <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/nl\/deling-van-veeltermen-voorbeelden-opgeloste-oefeningen-verdelen\/\">deling van polynomen<\/a><\/span><\/strong> wordt berekend, omdat het nu veel gemakkelijker voor je zal zijn om de procedure te leren (het is behoorlijk ingewikkeld).<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Potencia-de-un-monomio\"><\/span> De kracht van een monomial <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> <strong>Om de macht van een monomial te berekenen, wordt in de wiskunde elk element van de monomial verheven tot de exponent van de macht<\/strong> . Met andere woorden, de macht van een monomial bestaat uit het verhogen van de co\u00ebffici\u00ebnt en de variabelen (letters) ervan tot de exponent van de macht. <\/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\/puissance-dun-monome-exemple.png\" alt=\"hoe operaties met monomials worden opgelost\" class=\"wp-image-362\" width=\"179\" height=\"180\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Onthoud uit de eigenschappen van machten dat wanneer beide een toch al hoge term verhogen, exponenten zich vermenigvuldigen. Dit is de reden waarom <strong>, tot de macht van een monomial, de exponent van elke letter altijd wordt vermenigvuldigd met de exponent die de macht aangeeft<\/strong> .<\/p>\n<p> Aan de andere kant, om deze operatie correct uit te voeren, moet u de volgende eigenschap van bevoegdheden onthouden:<\/p>\n<ul>\n<li> Een negatieve monomial verhoogd tot een even exponent is gelijk aan een positieve monomial.<\/li>\n<li> In plaats daarvan resulteert een negatieve monomial verhoogd tot een oneven exponent in een negatieve monomial.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> Voorbeelden van bevoegdheden van monomials<\/h3>\n<p> We laten u enkele voorbeelden achter, zodat u duidelijk kunt begrijpen hoe de kracht van een monomial wordt berekend: <\/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-a1e51fcc4fe828722bfa6963d3540e08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(5x^6\\right)^2 = 5^2\\left(x^6\\right)^2 = 5^2x^{6\\cdot 2} = 25x^{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"268\" style=\"vertical-align: -7px;\"><\/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-488af8cc2d389d0a9012531e595a51e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(2x^5\\right)^4 = 2^4\\left(x^5\\right)^4 = 2^4x^{5\\cdot 4} = 16x^{20}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"268\" style=\"vertical-align: -7px;\"><\/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-931e60b61878fcf9dda31deb0eac0178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(-4y^3\\right)^2 = (-4)^2\\left(y^3\\right)^2 = (-4)^2y^{3\\cdot 2} = 16y^{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"326\" style=\"vertical-align: -7px;\"><\/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-43073f3940619cc05ddaf143d91031ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(3x^4y\\right)^3 = 3^3\\left(x^4y\\right)^3 = 3^3x^{4\\cdot 3}y^{1\\cdot 3} = 27x^{12}y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"331\" style=\"vertical-align: -7px;\"><\/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-841e3847493c3454e6e0cde2b389de9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(-2a^5b^7\\right)^3 = (-2)^3\\left(a^5b^7\\right)^3 = (-2)^3a^{5\\cdot 3}b^{7\\cdot 3} = -8a^{15}b^{21}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"417\" style=\"vertical-align: -7px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Operaciones-combinadas-con-monomios\"><\/span> Operaties gecombineerd met monomials<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Als je eenmaal hebt gezien wat alle bewerkingen met monomials zijn, weet dan dat ze ook met elkaar kunnen worden gecombineerd. Dat wil zeggen dat we oefeningen kunnen vinden waarin ons wordt gevraagd bewerkingen met monomialen op te lossen waarbij alle typen betrokken zijn: optellen, aftrekken, vermenigvuldigen, delen en machten.<\/p>\n<p> Maar maak je geen zorgen, ze zijn niet zo moeilijk als ze lijken. Het enige dat u hoeft te onthouden, is de volgorde waarin de gecombineerde bewerkingen worden opgelost:<\/p>\n<ol style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Ten eerste worden bewerkingen met monomialen tussen haakjes opgelost.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">Vervolgens worden de krachten van de monomialen berekend.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">Ten derde worden vermenigvuldigingen en delingen van monomialen uitgevoerd.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">En ten slotte worden de optellingen en aftrekkingen van monomialen bepaald.<\/span><\/li>\n<\/ol>\n<p> Ik ben er zeker van dat je door het oplossen van een voorbeeld het duidelijker zult zien:<\/p>\n<h3 class=\"wp-block-heading\"> Voorbeeld van gecombineerde werking van monomials<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ec50305026b5ae600feeedc2063ffb2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^9:(2x^4-8x^4)+3x^4\\cdot 6x - (x^3\\cdot 7x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Allereerst moeten we de bewerkingen met monomialen tussen haakjes oplossen:<\/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-20a79022126a4016bee178da5b2fd9a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^9:(-6x^4)+3x^4\\cdot 6x - 7x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"231\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> In dit geval hebben wij geen macht. Laten we nu de vermenigvuldigingen en delingen van monomialen berekenen:<\/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-75343501bfbe74ef63de85b90ce916c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x^5+18x^5 - 7x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"144\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> En ten slotte tellen we monomialen op en af: <\/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-b8dc32e179e406eb902f611c60ad1c0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"16x^5 - 7x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" 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-5da0d3692c51151ea9c2a0478ffaa720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{9x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-operaciones-con-monomios\"><\/span> Opgeloste oefeningen over operaties met monomials<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Als u wilt oefenen, laten we u hieronder verschillende oefeningen zien die stap voor stap zijn opgelost met de ESO-moeilijkheidsgraad bij operaties met monomials.<\/p>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Bereken de volgende optellingen en aftrekkingen van monomials: <\/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-1d2245ec403db8426a7c6747356beaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 2x^4+9x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"100\" 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-91d825e366ebde8630a08439cd57befe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -3x^5y^3 +4x^5y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"155\" 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-3f85bb7e0260af1c6e593b98fe852ad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 3x^8-6x^8+2x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"148\" 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-c0254b78b2cce547d32a5eac7675b5a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ -2a^3b^2-5a^3b^2+3a^3b^2-7a^3b^2+4a^3b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"340\" 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-864766b992d12d73d145c8075df256df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 6xyz-5xz-7xyz-8xz\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" 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-c83fa020e8457b4402f2b7da01617f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 6y^3+2y^3-y^5+8y^4-y^5-5y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"270\" 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>Zie de oplossing<\/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-56d30d2625c1f94ae6c667438b259524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 2x^4+9x^4= \\bm{11x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"160\" 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-4db7d7a7554cb1731e350df37305e936_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -3x^5y^3 +4x^5y^3= \\bm{x^5y^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" 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-598471a47e39a79742bf6e01dcbae7c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 3x^8-6x^8+2x^8= \\bm{-x^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"204\" 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-07daa6a36995cfe314093771fa52e921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ -2a^3b^2-5a^3b^2+3a^3b^2-7a^3b^2+4a^3b^2=\\bm{-7a^3b^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"419\" 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-ea6b3c423007edf6eee13c5fa69eafc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 6xyz-5xz-7xyz-8xz= \\bm{-xyz-13xz}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"345\" 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-7b81f9ed371675cfe8a51f608c3da025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 6y^3+2y^3-y^5+8y^4-y^5-5y^3 = \\bm{-2y^5+8y^4+3y^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"428\" 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\">Oefening 2<\/h3>\n<p> Los de volgende vermenigvuldigingen van monomialen op: <\/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-753999a2a1f5487e6842243827fddc38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 5x^7\\cdot 6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"92\" 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-facd1f9e25fe39a2f2ea7099c220faca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -4a^3 \\cdot (-2a)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"131\" 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-5a48b54dd3a3b028e42698709e3256ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 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-60d398af3d95ef228ed8404701bba1e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ -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-60666db89889355be28e2381482c2146_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 7x^3y^2 \\cdot 5x^8z^4 \\cdot (-2x^2y^5z^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"224\" 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>Zie de oplossing<\/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-462ca864ae7df79cca6d598a907ef47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 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-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-5b53bea16638f6a6d33c5ec2276a3e3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -4a^3 \\cdot (-2a) =(-4\\cdot (-2))a^{3+1} = \\bm{8a^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"324\" 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-88b62aecb02121fb27d5290456ae05cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 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-2738eff1187ab32a1f1d526051dce513_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ -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=\"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-d92004db2f9cc2fc28f7b5358dcb5932_l3.png\" height=\"131\" width=\"865\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\text{F)} \\ 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<h3 class=\"wp-block-heading\">Oefening 3<\/h3>\n<p> Bepaal het resultaat van de volgende verdelingen van monomials: <\/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-a538bc97a4e40a71e36ea49db97f40fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 24x^4: 6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"102\" 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-457fde039e753413817c083f0cb26ab5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 16a^9: (-2a^6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" 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-596179812c3d61c3aa87a965e1265aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -21x^3:(-3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"144\" 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-6a9a8fd439d22ab3a8f601ee400b758e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 14x^8y^3 :2x^6y\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" 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-61d294ce86a62652f898caad643e4aff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 42x^5y^3z^6 : 7x^2y^3z^4\" 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-de91d460fe9753ba75b7be2ad58e9599_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 48x^8y^6z^{10} : (-6x^4y^{2}z^4) : (-4x^2y^2z^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"305\" 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>Zie de oplossing<\/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-78e36b09fd9b819a65269c31c08da492_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 24x^4: 6x^2 = (24:6)x^{4-2} = \\bm{4x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" 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-0bcef3f5ee4e08629f22b3cb5fca73d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 16a^9: (-2a^6)= (16:(-2))a^{9-6} = \\bm{-8a^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"332\" 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-1d98b9bd4b6894c24bd28b2a4f0ff002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -21x^3:(-3x) = (-21:(-3))x^{3-1} = \\bm{7x^2}\" 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-5896be1f204d342ff20cbbe7bfa587a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 14x^8y^3 :2x^6y = \\bm{7x^2y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"196\" 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-8edc35d562476b2352abcba054635cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 42x^5y^3z^6 : 7x^2y^3z^4= 6x^3y^0z^2=\\bm{6x^3z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"320\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> In de vorige bewerking hebben we de term vereenvoudigd<\/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-c0f4ce4bf65bd54e5fc728271a7d7d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> omdat elk getal verhoogd tot 0 gelijk is aan 1. Dus: <\/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-07d692d378ec44f656fcde7667d5aab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^3y^0z^2=6x^3\\cdot 1 \\cdot z^2=\\bm{6x^3z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"228\" style=\"vertical-align: -4px;\"><\/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-1b1554d59ad6a39e24db564712789ee7_l3.png\" height=\"131\" width=\"618\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\text{F)} \\ 48x^8y^6z^{10} : (-6x^4y^{2}z^4) : (-4x^2y^2z^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-6dc0e068dbf84cef6abfe7e1789d245b_l3.png&quot; height=&quot;22&quot; width=&quot;194&quot; class=&quot;ql-img-displayed-equation quicklatex-auto-format&quot; alt=&quot;\\[-8x^4y^4z^6: (-4x^2y^2z^3)=\\]&quot; title=&quot;Rendered by QuickLaTeX.com&quot;\/> \\bm{2x^2y^2z^3}&#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<h3 class=\"wp-block-heading\">Oefening 4<\/h3>\n<p> Vind de volgende krachten van monomials: <\/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-3fd531461cb852f7cf8f4e4f6505c96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(-8x^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"93\" 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-9f74d8697d4ba1a59d074b73d2555430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(-2a^7\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"91\" 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-aca4350f00eb97562878ce29f48a96f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(5x^8y^2\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"96\" 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-1d9bcc48ef1555d5459cf28aa1abb3c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(-x^3y^5z\\right)^6\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"110\" 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-fe946ceee571ae61db828c15b6a47cbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ \\left(-2x^5y^4\\right)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"109\" style=\"vertical-align: -7px;\"><\/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>Zie de oplossing<\/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-20a7243c8e76a50f25b1da07921e231e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(-8x^4\\right)^2=(-8)^2\\left(x^4\\right)^2 = (-8)^2x^{4\\cdot 2} = \\bm{64x^{8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"361\" 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-718c9fcf2f66c2e2e7d874e80dc3a921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(-2a^7\\right)^3=(-2)^3\\left(a^7\\right)^3 = (-2)^3a^{7\\cdot 3} = \\bm{-8a^{21}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"368\" 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-71162deddf3bccc8fbc9107769152d4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(5x^8y^2\\right)^3=(5)^3\\left(x^8y^2\\right)^3 = \\bm{125x^{24}y^6}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"303\" 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-7eaa22bf4eb0e520c6ecdfa31c1585ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(-x^3y^5z\\right)^6=(-1)^6\\left(x^3y^5z\\right)^6 = \\bm{x^{18}y^{30}z^{6}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"338\" 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-c1f52fd47fc66e0f3178c63a0b864be8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ \\left(-2x^5y^4\\right)^5 =(-2)^5\\left(x^5y^4\\right)^5 = \\bm{-32x^{25}y^{20}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"342\" 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\">Oefening 5<\/h3>\n<p> Los de volgende bewerkingen op in combinatie met monomials en vereenvoudig ze zoveel mogelijk: <\/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-9c95dec30cc01c49200d9ce7e198edfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 3x^2\\cdot 4x^5 : 2x^4 + 10x^6:(-2x^4)\\cdot 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"292\" 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-bd210aaafaf98000f5ee202936c30d7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 4\\cdot \\left(5x^4 -2x^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"145\" 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-321e95fdde4c962fb0e532486180d6bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 8x^7:(-4x^3+3x^3-7x^3)-5x^3\\cdot 3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"298\" 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-981ccad0ae5f55e1d6d1db15b8aa2694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(-2x^2y\\right)^3+4x^2 \\cdot 5\\left(xy\\right)^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"277\" 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-1f33fd1cdef957f1e2818fa88968ea5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 8x^8:\\left(-2x^3\\right)^2-(7x^3\\cdot 6x^6): (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"301\" style=\"vertical-align: -7px;\"><\/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>Zie de oplossing<\/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-b5710afdc30e5dade5d481dad0d5cd77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{A}\\bm{)} \\color{black} \\ 3x^2\\cdot 4x^5 : 2x^4 + 10x^6:(-2x^4)\\cdot 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"366\" 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-485388f25e43e12a37c10f917feeca41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^7 : 2x^4 -5x^2\\cdot 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"156\" 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-3ee2fc488bcde1db8ffaa4326ac5b7d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^3 -30x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"83\" 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-89b11cc611350a670562c01e942c5415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-24x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" 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-01e9be21288169c2354a463f1c40361c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{B}\\bm{)} \\color{black} \\ 4\\cdot \\left(5x^4 -2x^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"219\" 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-1cc01826641601698450b1862bf36083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\left(3x^4 \\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"72\" 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-c970af842b560696a361e3380b8d3b7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot 9x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" 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alt=\"8x^7:(-8x^3)-5x^3\\cdot 3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"176\" 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-4a281b2cc5f0fb342b44088ce0813682_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x^4-15x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" 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-9ec10abaebfd5fdc5e42ccc865332f25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-16x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" 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-83f6044f7e0b53ec6897720463a94fde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{D}\\bm{)} \\color{black} \\ \\left(-2x^2y\\right)^3+4x^2 \\cdot 5\\left(xy\\right)^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"350\" 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-96d9d1b07bd2838d25894be6ccc8fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3+4x^2 \\cdot 5\\cdot x^4y^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"234\" 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-d4d6c7bf71a47be8084fd867bdf497ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3+4x^2 \\cdot 5x^4y^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" 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-79f03ec9d21f0dc8873f5bb951838d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3+20x^6y^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"190\" 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-c12ffd09529b975082bfe1f73098b7d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3-10x^6y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\"><\/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-63fd4ee3643afe01035c8189415c1e27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-18x^6y^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -4px;\"><\/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-603b9ac5ea94315d1329b4960dcb2f12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{E}\\bm{)} \\color{black} \\ 8x^8:\\left(-2x^3\\right)^2-(7x^3\\cdot 6x^6): (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"374\" 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-0453c3029ccff9ac02828970e9ee9c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^8:\\left(-2x^3\\right)^2-42x^9: (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"231\" 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-6cc9b09bf2b39f9ea04eb1b61587dfbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^8:4x^6-42x^9: (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" 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-474309bfcc65106dde914093f76f624c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{2x^2+21x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> De bewerking kan niet verder worden vereenvoudigd omdat de twee monomialen verschillende exponenten hebben, dus het resultaat is een polynoom.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Als je zo ver bent gekomen, betekent dit dat je alle handelingen met monomials al onder de knie hebt. Helder! Een andere bewerking die u zeker zal interesseren is de faculteit van een getal. Dit is een nogal merkwaardige operatie, omdat deze anders wordt berekend dan de andere. En in feite weten veel mensen niet wat de faculteit van een getal is. Ontdek hoe u een <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/nl\/faculteitsfunctie-van-een-getal\/\">faculteit<\/a><\/span><\/strong> kunt oplossen door op deze link te klikken.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Op deze pagina leggen we uit hoe je alle bewerkingen met monomialen uitvoert (optellen, aftrekken, vermenigvuldigen, delen en macht). Bovendien kunt u voorbeelden zien van elk type operatie met monomials en oefenen met oefeningen die stap voor stap worden opgelost. Optellen en aftrekken van monomials Twee of meer monomialen kunnen alleen worden opgeteld of afgetrokken &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/operaties-met-monomen-voorbeelden-en-oefeningen-opgelost-1-2-3-4-welke\/\"> <span class=\"screen-reader-text\">Operaties met monomials<\/span> Lees meer &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":[49],"tags":[],"class_list":["post-96","post","type-post","status-publish","format-standard","hentry","category-functie-representatie"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Operaties met monomials -<\/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\/nl\/operaties-met-monomen-voorbeelden-en-oefeningen-opgelost-1-2-3-4-welke\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Operaties met monomials -\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina leggen we uit hoe je alle bewerkingen met monomialen uitvoert (optellen, aftrekken, vermenigvuldigen, delen en macht). 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