{"id":347,"date":"2023-07-06T02:26:23","date_gmt":"2023-07-06T02:26:23","guid":{"rendered":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/"},"modified":"2023-07-06T02:26:23","modified_gmt":"2023-07-06T02:26:23","slug":"trinom-im-quadrat","status":"publish","type":"post","link":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/","title":{"rendered":"Trinomial im quadrat"},"content":{"rendered":"<p>Auf dieser Seite erkl\u00e4ren wir, wie man das Quadrat eines Trinoms (Formel) l\u00f6st. Dar\u00fcber hinaus k\u00f6nnen Sie mehrere Beispiele sehen und mit \u00dcbungen \u00fcben, die Schritt f\u00fcr Schritt zu quadrierten Trinomen gel\u00f6st werden. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-un-trinomio-al-cuadrado\"><\/span> Formel f\u00fcr ein quadriertes Trinom<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um die Trinom-Quadrat-Formel zu verstehen, m\u00fcssen Sie logischerweise zun\u00e4chst wissen, was ein <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/de\/trinom\/\">Trinom<\/a><\/span><\/strong> ist. Ich hinterlasse Ihnen diesen Link f\u00fcr den Fall, dass Sie ihn \u00fcberpr\u00fcfen m\u00f6chten, bevor Sie mit der Erkl\u00e4rung fortfahren.<\/p>\n<p> Ein <strong>Trinomquadrat<\/strong> ist gleich dem Quadrat des ersten Termes, plus dem Quadrat des zweiten Termes, plus dem Quadrat des dritten Termes, plus dem Doppelten des ersten Termes mal dem zweiten, plus dem Doppelten des ersten Termes mal dem dritten, plus dem Doppelten Zweiter f\u00fcr den Dritten. <\/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\/carre-dun-trinome.png\" alt=\"Quadrat eines Trinoms oder Trinomquadrat\" class=\"wp-image-2847\" width=\"378\" height=\"302\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Das Quadrat eines Trinoms ist so wichtig, weil es ein bemerkenswertes Produkt (oder eine bemerkenswerte Identit\u00e4t) ist, das hei\u00dft, es gibt eine mathematische Formel, mit der Sie diese Operation schnell berechnen k\u00f6nnen. Klicken Sie auf den folgenden Link, um alle <a href=\"https:\/\/mathority.org\/de\/identitaten,-produkte,-bemerkenswerte-gleichheiten,-geloste-ubungen\/\"><strong><span style=\"text-decoration: underline;\">wichtigen Produktformeln<\/span><\/strong><\/a> anzuzeigen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-trinomios-al-cuadrado\"><\/span> Beispiele f\u00fcr quadratische Trinome<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nachdem wir gesehen haben, wie die Formel f\u00fcr ein quadriertes Trinom lautet, werden wir mehrere Beispiele f\u00fcr die Berechnung des Quadrats eines Trinoms sehen:<\/p>\n<h3 class=\"wp-block-heading\"> Beispiel 1<\/h3>\n<ul>\n<li> Berechnen Sie die folgende Potenz eines quadrierten Trinoms:<\/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-7ee4db6a5192b7efea2342d21275e487_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2+x+3\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"101\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Die Formel f\u00fcr das Quadrat eines Trinoms lautet:<\/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-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Daher m\u00fcssen wir zun\u00e4chst die Parameterwerte identifizieren<\/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-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a,b\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\"><\/p>\n<p> Und<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> der Formel. In dieser \u00dcbung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ost<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f6edd3d7af07ab26b4a0a71c20c0b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p> der Koeffizient<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> entsprechen dem<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> Und<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> ist der unabh\u00e4ngige Term 3:<\/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-55e06f44486e75e9153a60d36e83bc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} (a+b+c)^2\\\\[2ex] \\left(x^2+x+3\\right)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x^2 \\\\[2ex] b=x \\\\[2ex] c=3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"90\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Und wenn wir die Werte bereits kennen, setzen Sie diese Werte einfach in die Formel ein und f\u00fchren Sie die Berechnungen durch: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-trinome-au-carre.png\" alt=\"Beispiel f\u00fcr ein quadratisches Trinom\" class=\"wp-image-2850\" width=\"643\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Andererseits ist zu beachten, dass ein quadratisches Trinom nicht dasselbe ist wie <a href=\"https:\/\/mathority.org\/de\/perfektes-quadratisches-trinom\/\"><strong><span style=\"text-decoration: underline;\">ein perfektes quadratisches Trinom<\/span><\/strong><\/a> . Dies ist ein h\u00e4ufiger Fehler, da viele Menschen diese beiden Konzepte verwechseln. Sie k\u00f6nnen die Unterschiede zwischen diesen beiden Arten von Trinomen unter dem Link in diesem Absatz sehen.<\/p>\n<h3 class=\"wp-block-heading\"> Beispiel 2<\/h3>\n<ul>\n<li> Finden Sie das n\u00e4chste Quadrat eines Trinoms:<\/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-c6ced36e156a021e512b73f322138074_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2-2x+4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"110\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Um diese Polynompotenz zu bestimmen, m\u00fcssen wir die Formel f\u00fcr ein auf zwei erh\u00f6htes Trinom anwenden:<\/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-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Bei diesem Problem gilt:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dies entspricht<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f6edd3d7af07ab26b4a0a71c20c0b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> entspricht dem negativen Monom<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae405991eecf234826df9d5bbfb8de4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\"><\/p>\n<p> Und<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> ist Nummer 4:<\/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-e816dc27154d8b4e9748c340da4a04e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} (a+b+c)^2\\\\[2ex] \\left(x^2-2x+4\\right)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x^2 \\\\[2ex] b=-2x \\\\[2ex] c=4 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"90\" width=\"366\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Also setzen wir die gefundenen Werte in die Formel ein und l\u00f6sen die resultierenden Operationen:<\/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-97cdd6092e40172071bcb1e84b4df444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l} \\left(x^2-2x+4\\right)^2 = \\\\[2ex] = \\left(x^2\\right)^2+(-2x)^2+4^2+2\\cdot x^2 \\cdot (-2x) + 2 \\cdot x^2 \\cdot 4 +2 \\cdot (-2x) \\cdot 4 = \\\\[2ex] = x^4+4x^2+16-4x^3 + 8x^2 -16x = \\\\[2ex] = x^4-4x^3+12x^2-16x+16 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"508\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Denken Sie daran, dass die Potenz mit einem geraden Exponenten einer negativen Basis einen positiven Term ergibt, also<\/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-e252311ea5bbe33f6b3f066ed805d4a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-2x)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<p> ist gleich<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dac0d6c1d060e62694d182231bd81d82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Nachdem Sie nun gesehen haben, wie das Quadrat eines Trinoms berechnet wird, wird es Sie wahrscheinlich auch interessieren, wie man das <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/de\/formel-fur-das-produkt-der-summe-mit-der-differenz\/\">Produkt der Summe durch die Differenz<\/a><\/span><\/strong> zweier Terme l\u00f6st. Tats\u00e4chlich geh\u00f6rt er zu den Top 3 der bemerkenswertesten (wichtigsten) Identit\u00e4ten. Wie die Formel lautet und wie sie angewendet wird, k\u00f6nnen Sie auf der verlinkten Seite sehen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-cuadrado-de-un-trinomio\"><\/span> Demonstration der Formel f\u00fcr das Quadrat eines Trinoms<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um den Begriff der Potenz eines Trinomquadrats vollst\u00e4ndig zu verstehen, werden wir die Formel herleiten, die wir gerade studiert haben.<\/p>\n<p> Von jedem auf 2 angehobenen Trinom:<\/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-379affdd0954c4ca08ed08041e0eb7b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Der obige algebraische Ausdruck entspricht der Multiplikation des Trinoms in Klammern mit sich selbst:<\/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-d8944601270bfee61c23bb9440e7fd79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2 = (a+b+c)(a+b+c)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"275\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Nun multiplizieren wir die beiden Trinome:<\/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-ceaddc98a341af8c426098e15affbe7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)(a+b+c)= a^2+ab+ac+ba+b^2+bc+ca+cb+c^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"505\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Abschlie\u00dfend gruppieren wir \u00e4hnliche Begriffe:<\/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-79d99fd9567501331249064ee77e6db1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2+ab+ac+ba+b^2+bc+ca+cb+c^2 = a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"576\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Und damit sind wir bereits beim Ausdruck der Formel angelangt, so dass die Formel f\u00fcr das Quadrat eines Trinoms demonstriert wird:<\/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-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Auf unserer Website haben wir weitere Demonstrationen bemerkenswerter Identit\u00e4ten. Sie k\u00f6nnen sich beispielsweise die Demonstration der Formel f\u00fcr eine <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/de\/quadrat-einer-summe-oder-summe-im-quadrat\/\">quadrierte Summe<\/a><\/span><\/strong> und eine <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/de\/quadrat-einer-differenz-oder-subtraktion\/\">quadrierte Differenz<\/a><\/span><\/strong> ansehen. Dar\u00fcber hinaus sehen Sie in diesen Links nicht nur ihre Beweise, sondern auch die geometrische Interpretation ihrer Formeln, also was diese Art bemerkenswerter Identit\u00e4ten geometrisch bedeuten. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-trinomios-al-cuadrado\"><\/span> Probleme mit quadratischen Trinomen gel\u00f6st<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> L\u00f6sen Sie die folgenden quadratischen Trinome: <\/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-b1e2db1dacfd70bcdf33589968427633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(x^2+x+5\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"132\" 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-6eddfbe2255cd7f5b8d829ff6aef4e38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(x^2+3x-4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"141\" 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-577a572f8974257e1d6d7b8411f75f4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(4x^2-6x+3\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"150\" 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-4a26869f17cf7889324d3d5e6755b800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(x^3-3x^2-9x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"159\" 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>siehe L\u00f6sung<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Um alle Aufgaben zu l\u00f6sen, m\u00fcssen wir die Formel f\u00fcr das Quadrat eines Trinoms verwenden, die lautet: <\/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-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" 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-749dc45e7a00d7122d62b774706bdcc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{array}{l} \\left(x^2+x+5\\right)^2 = \\\\[2ex] = \\left(x^2\\right)^2+x^2+5^2+2\\cdot x^2 \\cdot x + 2 \\cdot x^2 \\cdot 5 +2 \\cdot x \\cdot 5 = \\\\[2ex] = x^4+x^2+25+2x^3 + 10x^2 +10x = \\\\[2ex] = \\bm{x^4+2x^3+11x^2+10x+25} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"438\" 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-b1f51f18b3c1118b6e8e3acc3441b0ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{array}{l}\\left(x^2+3x-4\\right)^2 = \\\\[2ex] = \\left(x^2\\right)^2+(3x)^2+(-4)^2+2\\cdot x^2 \\cdot 3x + 2 \\cdot x^2 \\cdot (-4) +2 \\cdot 3x \\cdot (-4) = \\\\[2ex] = x^4+9x^2+16+6x^3-8x^2-24x = \\\\[2ex] = \\bm{x^4+6x^3+x^2-24x+16} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"557\" 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-49c6496bf684296d315fc96d9cb5857e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{array}{l}\\left(4x^2-6x+3\\right)^2 = \\\\[2ex] = \\left(4x^2\\right)^2+(-6x)^2+3^2+2\\cdot 4x^2 \\cdot (-6x) + 2 \\cdot 4x^2 \\cdot 3 +2 \\cdot (-6x) \\cdot 3 = \\\\[2ex] = 16x^4+36x^2+9-48x^3+24x^2-36x = \\\\[2ex] = \\bm{16x^4-48x^3+60x^2-36x+9} \\end{array}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"570\" 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-7cd08035d8402c27c411bcf5b30216cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{array}{l}  \\left(x^3-3x^2-9x\\right)^2 = \\\\[2ex] = \\left(x^3\\right)^2+\\left(-3x^2\\right)^2+(-9x)^2+2\\cdot x^3 \\cdot (-3x^2) + 2 \\cdot x^3 \\cdot (-9x) +2 \\cdot (-3x^2) \\cdot (-9x) = \\\\[2ex] = x^6+9x^4+81x^2-6x^5-18x^4+54x^3 = \\\\[2ex] = \\bm{x^6-6x^5-9x^4+54x^3+81x^2} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"682\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Auf dieser Seite erkl\u00e4ren wir, wie man das Quadrat eines Trinoms (Formel) l\u00f6st. Dar\u00fcber hinaus k\u00f6nnen Sie mehrere Beispiele sehen und mit \u00dcbungen \u00fcben, die Schritt f\u00fcr Schritt zu quadrierten Trinomen gel\u00f6st werden. Formel f\u00fcr ein quadriertes Trinom Um die Trinom-Quadrat-Formel zu verstehen, m\u00fcssen Sie logischerweise zun\u00e4chst wissen, was ein Trinom ist. Ich hinterlasse Ihnen &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\"> <span class=\"screen-reader-text\">Trinomial im quadrat<\/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":[10],"tags":[],"class_list":["post-347","post","type-post","status-publish","format-standard","hentry","category-bemerkenswerte-identitaten"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Trinomial im Quadrat - Mathematik<\/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\/de\/trinom-im-quadrat\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trinomial im Quadrat - Mathematik\" \/>\n<meta property=\"og:description\" content=\"Auf dieser Seite erkl\u00e4ren wir, wie man das Quadrat eines Trinoms (Formel) l\u00f6st. Dar\u00fcber hinaus k\u00f6nnen Sie mehrere Beispiele sehen und mit \u00dcbungen \u00fcben, die Schritt f\u00fcr Schritt zu quadrierten Trinomen gel\u00f6st werden. Formel f\u00fcr ein quadriertes Trinom Um die Trinom-Quadrat-Formel zu verstehen, m\u00fcssen Sie logischerweise zun\u00e4chst wissen, was ein Trinom ist. Ich hinterlasse Ihnen &hellip; Trinomial im quadrat Weiterlesen &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T02:26:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-dun-trinome.png\" \/>\n<meta name=\"author\" content=\"Mathority Mannschaft\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Verfasst von\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mathority Mannschaft\" \/>\n\t<meta name=\"twitter:label2\" content=\"Gesch\u00e4tzte Lesezeit\" \/>\n\t<meta name=\"twitter:data2\" content=\"3\u00a0Minuten\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\"},\"author\":{\"name\":\"Mathority Mannschaft\",\"@id\":\"https:\/\/mathority.org\/de\/#\/schema\/person\/c7da97cc1c90fc5e022a3dd06a76d3be\"},\"headline\":\"Trinomial im quadrat\",\"datePublished\":\"2023-07-06T02:26:23+00:00\",\"dateModified\":\"2023-07-06T02:26:23+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\"},\"wordCount\":639,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/de\/#organization\"},\"articleSection\":[\"Bemerkenswerte identit\u00e4ten\"],\"inLanguage\":\"de\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\",\"url\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\",\"name\":\"Trinomial im Quadrat - Mathematik\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/de\/#website\"},\"datePublished\":\"2023-07-06T02:26:23+00:00\",\"dateModified\":\"2023-07-06T02:26:23+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#breadcrumb\"},\"inLanguage\":\"de\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/de\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Trinomial im quadrat\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/de\/#website\",\"url\":\"https:\/\/mathority.org\/de\/\",\"name\":\"Mathority\",\"description\":\"Wo Neugierde auf Berechnung trifft!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/de\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/de\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"de\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/de\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/de\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de\",\"@id\":\"https:\/\/mathority.org\/de\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/de\/wp-content\/uploads\/2023\/09\/mathority-log.png\",\"contentUrl\":\"https:\/\/mathority.org\/de\/wp-content\/uploads\/2023\/09\/mathority-log.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/de\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/de\/#\/schema\/person\/c7da97cc1c90fc5e022a3dd06a76d3be\",\"name\":\"Mathority Mannschaft\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de\",\"@id\":\"https:\/\/mathority.org\/de\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Mathority Mannschaft\"},\"sameAs\":[\"http:\/\/mathority.org\/de\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Trinomial im Quadrat - Mathematik","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/","og_locale":"de_DE","og_type":"article","og_title":"Trinomial im Quadrat - Mathematik","og_description":"Auf dieser Seite erkl\u00e4ren wir, wie man das Quadrat eines Trinoms (Formel) l\u00f6st. Dar\u00fcber hinaus k\u00f6nnen Sie mehrere Beispiele sehen und mit \u00dcbungen \u00fcben, die Schritt f\u00fcr Schritt zu quadrierten Trinomen gel\u00f6st werden. Formel f\u00fcr ein quadriertes Trinom Um die Trinom-Quadrat-Formel zu verstehen, m\u00fcssen Sie logischerweise zun\u00e4chst wissen, was ein Trinom ist. Ich hinterlasse Ihnen &hellip; Trinomial im quadrat Weiterlesen &raquo;","og_url":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/","article_published_time":"2023-07-06T02:26:23+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-dun-trinome.png"}],"author":"Mathority Mannschaft","twitter_card":"summary_large_image","twitter_misc":{"Verfasst von":"Mathority Mannschaft","Gesch\u00e4tzte Lesezeit":"3\u00a0Minuten"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/"},"author":{"name":"Mathority Mannschaft","@id":"https:\/\/mathority.org\/de\/#\/schema\/person\/c7da97cc1c90fc5e022a3dd06a76d3be"},"headline":"Trinomial im quadrat","datePublished":"2023-07-06T02:26:23+00:00","dateModified":"2023-07-06T02:26:23+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/"},"wordCount":639,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/de\/#organization"},"articleSection":["Bemerkenswerte identit\u00e4ten"],"inLanguage":"de","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/de\/trinom-im-quadrat\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/","url":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/","name":"Trinomial im Quadrat - Mathematik","isPartOf":{"@id":"https:\/\/mathority.org\/de\/#website"},"datePublished":"2023-07-06T02:26:23+00:00","dateModified":"2023-07-06T02:26:23+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#breadcrumb"},"inLanguage":"de","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/de\/trinom-im-quadrat\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/de\/trinom-im-quadrat\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/de\/"},{"@type":"ListItem","position":2,"name":"Trinomial im quadrat"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/de\/#website","url":"https:\/\/mathority.org\/de\/","name":"Mathority","description":"Wo Neugierde auf Berechnung trifft!","publisher":{"@id":"https:\/\/mathority.org\/de\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/de\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"de"},{"@type":"Organization","@id":"https:\/\/mathority.org\/de\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/de\/","logo":{"@type":"ImageObject","inLanguage":"de","@id":"https:\/\/mathority.org\/de\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/de\/wp-content\/uploads\/2023\/09\/mathority-log.png","contentUrl":"https:\/\/mathority.org\/de\/wp-content\/uploads\/2023\/09\/mathority-log.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/de\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/de\/#\/schema\/person\/c7da97cc1c90fc5e022a3dd06a76d3be","name":"Mathority Mannschaft","image":{"@type":"ImageObject","inLanguage":"de","@id":"https:\/\/mathority.org\/de\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Mathority Mannschaft"},"sameAs":["http:\/\/mathority.org\/de"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/posts\/347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/comments?post=347"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/posts\/347\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/media?parent=347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/categories?post=347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/de\/wp-json\/wp\/v2\/tags?post=347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}