{"id":332,"date":"2023-07-06T06:56:12","date_gmt":"2023-07-06T06:56:12","guid":{"rendered":"https:\/\/mathority.org\/de\/quadrat-einer-differenz-oder-subtraktion\/"},"modified":"2023-07-06T06:56:12","modified_gmt":"2023-07-06T06:56:12","slug":"quadrat-einer-differenz-oder-subtraktion","status":"publish","type":"post","link":"https:\/\/mathority.org\/de\/quadrat-einer-differenz-oder-subtraktion\/","title":{"rendered":"Quadrat einer differenz (oder subtraktion)"},"content":{"rendered":"<p>Hier erkl\u00e4ren wir, was die bemerkenswerte Identit\u00e4tsformel des Quadrats einer Differenz (oder Subtraktion) ist, das hei\u00dft, wir zeigen Ihnen, wie der Ausdruck (ab) <sup>2<\/sup> gel\u00f6st wird. Dar\u00fcber hinaus k\u00f6nnen Sie Beispiele sehen und mit \u00dcbungen \u00fcben, die zum Quadrat der Differenz gel\u00f6st werden. Und schlie\u00dflich zeigen wir die Formeldemonstration und geometrische Interpretation dieses bemerkenswerten Produkttyps. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-cuadrado-de-una-diferencia-o-resta\"><\/span> Was ist das Quadrat einer Differenz (oder Subtraktion)?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Das <strong>Quadrat einer Differenz<\/strong> oder <strong>das Quadrat einer Subtraktion<\/strong> ist eine der <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/de\/identitaten,-produkte,-bemerkenswerte-gleichheiten,-geloste-ubungen\/\">bemerkenswerten Identit\u00e4ten<\/a><\/span><\/strong> (oder bemerkenswerten Produkte), das hei\u00dft, es besteht aus einer mathematischen Regel, die die Berechnung der Quadratur eines Binomials mit zwei Termen erleichtert: einem positiven und das andere negativ.<\/p>\n<p> Daher ist der algebraische Ausdruck f\u00fcr das Quadrat einer Differenz <strong>(ab) <sup>2<\/sup><\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-cuadrado-de-una-diferencia-o-resta\"><\/span> Formel f\u00fcr das Quadrat einer Differenz (oder Subtraktion)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sobald wir die Definition dieser Art bemerkenswerter Identit\u00e4t gesehen haben, werden wir sehen, wie man das Quadrat einer Differenz mit ihrer Formel l\u00f6st: <\/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\/formule-du-carre-dune-difference-ou-soustraction.png\" alt=\"Formel f\u00fcr das Quadrat einer Differenz oder Subtraktion\" class=\"wp-image-2407\" width=\"299\" height=\"300\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <strong>Damit ist das Quadrat einer Differenz gleich dem Quadrat des ersten Termes, minus dem doppelten Produkt des ersten mit dem zweiten, plus dem Quadrat des zweiten.<\/strong><\/p>\n<p> Um also eine Differenz oder eine quadrierte Subtraktion zu berechnen, m\u00fcssen Sie nicht nur jeden Term auf zwei erh\u00f6hen, sondern sie auch miteinander und mit 2 multiplizieren.<\/p>\n<p> Dies ist wichtig zu beachten, da ein sehr h\u00e4ufiger Fehler beim Subtrahieren von Quadraten darin besteht, nicht das Produkt zwischen den beiden Termen zu bilden und nur das Quadrat der Abnahme und die Subtraktion der Subtraktion zu l\u00f6sen: <\/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-du-binome-d-une-soustraction.jpg\" alt=\"Quadrat des Binomials einer Subtraktion\" class=\"wp-image-2409\" width=\"235\" height=\"66\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Vergessen Sie nicht das Produkt zwischen a und b! <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-cuadrados-de-diferencias-o-restas\"><\/span> Beispiele f\u00fcr Differenzquadrate (oder Subtraktionsquadrate).<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Da wir nun die Formel f\u00fcr das Quadrat einer Differenz kennen, k\u00f6nnen wir damit Berechnungen durchf\u00fchren. Und damit Sie sehen k\u00f6nnen, wie das geht, haben wir mehrere gel\u00f6ste Beispiele f\u00fcr das Quadrat einer Differenz (oder Subtraktion) vorbereitet.<\/p>\n<h3 class=\"wp-block-heading\"> Beispiel 1<\/h3>\n<ul>\n<li> L\u00f6sen Sie die folgende Differenz im Quadrat:<\/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-c639502958a3e7b758e74eda141cd322_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-3)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Da es sich um eine quadrierte Subtraktion handelt, m\u00fcssen Sie die Formel 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-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Wir m\u00fcssen also die Werte der Unbekannten ermitteln<\/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> Und<\/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> der Formel. In diesem Fall,<\/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> ist die Variable<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Und<\/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 Nummer 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-1bb2d14a30d2cdabae6458f5df32392a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a-b)^2\\\\[2ex] (x-3)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x \\\\[2ex] b=3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Beachten Sie, dass das negative Vorzeichen nicht Teil von ist<\/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-a521efcd0a946cd643aebe98b5b41a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> Sie m\u00fcssen jedoch immer die Zahl ohne Vorzeichen nehmen, um die Formel richtig anzuwenden.<\/p>\n<p> Wir kennen daher bereits die Werte von<\/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> und von<\/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> Daher m\u00fcssen wir nur diese Werte in die Formel einsetzen: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome-dune-soustraction-au-carre-exercices-resolus.jpg\" alt=\"\u00dcbungen zur binomischen Subtraktion im Quadrat gel\u00f6st\" class=\"wp-image-2417\" width=\"299\" height=\"173\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> Beispiel 2<\/h3>\n<ul>\n<li> Berechnen Sie das folgende Binomial einer quadrierten Subtraktion:<\/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-4a94d5ee509fb5d8e9eaf9a633f36f46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(5x-2)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Die Formel f\u00fcr die quadrierte Differenz 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-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Wir m\u00fcssen also zun\u00e4chst die Werte von 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-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> und von<\/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> der Formel. Bei diesem Problem gilt:<\/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> stellt das Monom dar<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6093d29b7c98d4d53162882fe6703e10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\"><\/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-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> ist \u00e4quivalent zum unabh\u00e4ngigen Term des Binomials, also 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-868a41eb665f5bc94959448547c060d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a-b)^2\\\\[2ex] (5x-2)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=5x \\\\[2ex] b=2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Schlie\u00dflich kennen wir den Wert der Parameter<\/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> Und<\/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> , wenden wir einfach die Binomialformel f\u00fcr die quadrierte Subtraktion an: <\/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-a5e88231a654b23a306e53e17d175d25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (5x-2)^2 &amp; = (5x)^2-2\\cdot 5x \\cdot 2 + 2^2 \\\\[2ex] &amp; = 25x^2-20x+4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"256\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-cuadrado-de-una-diferencia\"><\/span> Beweis der Formel f\u00fcr das Quadrat einer Differenz<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Wir werden dann ableiten, woher die Formel f\u00fcr das Quadrat einer Subtraktion kommt. Obwohl Sie sich den Beweis nicht merken m\u00fcssen, ist es dennoch sch\u00f6n, die Mathematik dahinter zu verstehen.<\/p>\n<p> Wenn wir vom Ausdruck des Binomials aller Subtraktionen ausgehen:<\/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-8f88949b2f3fcc20e9d00f495e471cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Offensichtlich ist die vorherige Potenz gleich dem Produkt des Faktors<\/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-5ab5e2adaf0a63382c066ea55b51147c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<p> mit sich selbst multipliziert:<\/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-5786e5179724339feaef50ccdb33ead1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2= (a-b)\\cdot (a-b)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Jetzt multiplizieren wir die beiden Klammern, indem wir die Verteilungseigenschaft 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-3b46073fd758d93fff8956f0a8dd57af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(a-b)\\cdot (a-b) &amp; = a\\cdot a +a\\cdot (-b) - b\\cdot a - b \\cdot (-b) \\\\[2ex] &amp; = a^2-ab-ba+b^2 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Und wir m\u00fcssen nur noch \u00e4hnliche Begriffe zusammenfassen, um den Beweis der Formel abzuschlie\u00dfen:<\/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-68a1e26dd180891fc1ee31584a471ca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2-ab-ba+b^2 = a^2-2ab +b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"256\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Damit die Formel f\u00fcr das Quadrat einer Subtraktion mathematisch bewiesen werden kann:<\/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-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kurioserweise wird die Entwicklung des Binomialausdrucks einer quadrierten Subtraktion auch als perfektes quadratisches Trinom bezeichnet. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpretacion-geometrica-del-cuadrado-de-una-diferencia\"><\/span> Geometrische Interpretation des Quadrats einer Differenz<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um den Begriff des Quadrats einer Differenz vollst\u00e4ndig zu verstehen, werden wir sehen, wie wir diese bemerkenswerte Gleichheit geometrisch interpretieren k\u00f6nnen.<\/p>\n<p> Schauen Sie sich das folgende Quadrat mit Seitenl\u00e4nge an <\/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-4fad90838c7fa310bdbea2364787ced6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/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\/interpretation-geometrique-du-carre-de-la-difference.jpg\" alt=\"geometrische Interpretation des Quadrats einer Differenz\" class=\"wp-image-2427\" width=\"321\" height=\"321\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Die Fl\u00e4che (oder Oberfl\u00e4che) eines Quadrats oder Rechtecks wird durch Multiplikation zweier benachbarter Seiten berechnet. Daher betr\u00e4gt die Fl\u00e4che des gesamten ganzzahligen Quadrats oben<\/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-217fa12aa2b62c902c84fa81b873991a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\\cdot a = a^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ebenso ist die Fl\u00e4che jedes gelben Rechtecks gleich<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6598b0081ed8a7b827b59324acfae35a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\\cdot b = ab.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<p> Und schlie\u00dflich hat das kleine Quadrat oben rechts eine Fl\u00e4che von<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4eeba14a61903733ce2d13bcf35d3ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\\cdot b =b^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dies bedeutet, dass ein Quadrat eine Seite hat<\/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-62727d3bc0a05c70472ae09eba377396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b),\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<p> deren Oberfl\u00e4che ist<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff46b79cf0127ee95c26509e5c5c957c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -5px;\"><\/p>\n<p> kann in die Fl\u00e4che eines Dimensionsquadrats zerlegt werden<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8fa4ffebd0bdc66a5e68aa7b712f46c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> minus 2 mal die Fl\u00e4che eines Rechtecks mit Abmessungen<\/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> Und<\/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> , plus der Fl\u00e4che eines Seitenquadrats<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf59029b62b61185814b66fa6004b2f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> Kurz gesagt, die Formel f\u00fcr das Quadrat einer Differenz l\u00e4sst sich auch geometrisch verifizieren: <\/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-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-cuadrado-de-una-diferencia-o-resta\"><\/span> Gel\u00f6ste Probleme des Quadrats einer Differenz (oder Subtraktion)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Damit Sie \u00fcben k\u00f6nnen, stellen wir Ihnen mehrere \u00dcbungen zur Verf\u00fcgung, die Schritt f\u00fcr Schritt zum bemerkenswerten Produkt des Quadrats einer Differenz gel\u00f6st werden. Denken Sie daran, dass Sie uns alle Fragen, die Sie haben, unten in den Kommentaren schreiben k\u00f6nnen.<\/p>\n<h3 class=\"wp-block-heading\"> \u00dcbung 1<\/h3>\n<p> L\u00f6sen Sie die folgenden Subtraktionen im Quadrat: <\/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-4c11a4f53553874acb14ec9bbd0c78d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x-2)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55330f15a13171e004a6fd9063b5042d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ (3-7x)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"96\" 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-9a9afedffeffbe27f4e9c5d94b2bcad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(x^2-6\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"100\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f96b2af0d8ddde63f0f5ff04acde9e8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (-3x+y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"111\" 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-1d4b37f1b9fc0170cdcdf8ff4a136e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ (4x-3y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"105\" 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>siehe L\u00f6sung<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Um alle bemerkenswerten Identit\u00e4ten des Problems zu finden, reicht es aus, die Formel f\u00fcr das Quadrat einer Differenz anzuwenden, 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-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" 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-14d502eda968fe82617b4403cd9c4722_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}(x-2)^2&amp; =x^2-2\\cdot x\\cdot 2 +2^2\\\\[2ex] &amp; = \\bm{x^2-4x +4}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"248\" 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-c22d520301280872e645f5683a2fba8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}(3-7x)^2 &amp; =3^2-2\\cdot 3\\cdot 7x +(7x)^2\\\\[2ex] &amp; = \\bm{9-42x+49x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"288\" 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-95c7c481a96b20b700bd2253c90f0c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned}\\left(x^2-6\\right)^2 &amp; = \\left(x^2\\right)^2-2\\cdot x^2\\cdot 6 +6^2\\\\[2ex] &amp; = \\bm{x^4-12x^2 +36}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"66\" width=\"290\" 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-3cea9fa89580d3d9d9df7fd93cca2b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned}(-3x+y)^2 &amp; = (y-3x)^2 \\\\[2ex] &amp; = y^2-2\\cdot y\\cdot 3x +(3x)^2\\\\[2ex] &amp; = \\bm{y^2-6yx+9x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"304\" 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-138b359ce2e8f8b1012c6ecf1b7fb9b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ \\begin{aligned}(4x-3y)^2 &amp; = (4x)^2-2\\cdot 4x\\cdot 3y +(3y)^2\\\\[2ex] &amp; = \\bm{16x^2-24xy+9y^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"329\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u00dcbung 2<\/h3>\n<p> Bestimmen Sie die folgenden Quadrate der Differenzen zweier Gr\u00f6\u00dfen, indem Sie die Formel 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-2d817b4488d40c395b508191a9257bf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(6x^3-4y^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"127\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b93817974b7ab8b03fa60852c85e570a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\displaystyle \\left(\\sqrt{2x}-\\sqrt{8x}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"146\" style=\"vertical-align: -11px;\"><\/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-5ce347a33830b600df805f9b3089a629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\left(\\frac{5}{2}x^2-\\frac{4}{5}x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"137\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>siehe L\u00f6sung<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Um alle nennenswerten Produkte des Problems zu bestimmen, muss die Formel f\u00fcr eine quadrierte Subtraktion verwendet werden: <\/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-3074d6e8bc69734f38234657d1fddc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2=a^2-2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" 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-c73b9ba584f955a0cae5564a2226d465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}\\left(6x^3-4y^4\\right)^2 &amp; =\\left(6x^3\\right)^2-2\\cdot 6x^3\\cdot 4y^4 +\\left(4y^4\\right)^2\\\\[2ex] &amp; = \\bm{36x^6-48x^3y^4+16y^8}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Um Abschnitt B) zu l\u00f6sen, m\u00fcssen Sie bedenken, dass das Quadratieren einer Wurzel vereinfacht 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-38cd9e9855f7f79f607247ccc731e297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(\\sqrt{2x}-\\sqrt{8x}\\right)^2 &amp; =\\left(\\sqrt{2x}\\right)^2-2\\cdot \\sqrt{2x}\\cdot \\sqrt{8x} +\\left(\\sqrt{8x}\\right)^2\\\\[2ex] &amp; =2x-2\\sqrt{2x\\cdot 8x} +8x \\\\[2ex] &amp; = 10x-2\\sqrt{16x^2} \\\\[2ex] &amp;= 10x-2\\cdot 4x = \\\\[2ex] &amp; = 10x -8x \\\\[2ex] &amp; = \\bm{2x}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"247\" width=\"443\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Die Monome der letzten quadrierten Subtraktion haben Bruchkoeffizienten, daher m\u00fcssen wir zur L\u00f6sung die Eigenschaften von Br\u00fcchen verwenden: <\/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-46106420913cc7a370e2f5215af0f2a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\begin{aligned} \\left(\\frac{5}{2}x^2-\\frac{4}{5}x\\right)^2 &amp; = \\left(\\frac{5}{2}x^2\\right)^2-2\\cdot \\frac{5}{2}x^2\\cdot \\frac{4}{5}x +\\left(\\frac{4}{5}x\\right)^2\\\\[2ex] &amp; = \\frac{5^2}{2^2}x^4-2\\cdot \\frac{20}{10}x^3 +\\frac{4^2}{5^2}x^2 \\\\[2ex] &amp;= \\frac{25}{4}x^4 -2\\cdot 2x^3+\\frac{16}{25}x^2 \\\\[2ex] &amp; = \\mathbf{\\frac{25}{4}} \\bm{x^4-4x^3+}\\mathbf{\\frac{16}{25}}\\bm{x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"416\" 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>Hier erkl\u00e4ren wir, was die bemerkenswerte Identit\u00e4tsformel des Quadrats einer Differenz (oder Subtraktion) ist, das hei\u00dft, wir zeigen Ihnen, wie der Ausdruck (ab) 2 gel\u00f6st wird. Dar\u00fcber hinaus k\u00f6nnen Sie Beispiele sehen und mit \u00dcbungen \u00fcben, die zum Quadrat der Differenz gel\u00f6st werden. Und schlie\u00dflich zeigen wir die Formeldemonstration und geometrische Interpretation dieses bemerkenswerten Produkttyps. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/de\/quadrat-einer-differenz-oder-subtraktion\/\"> <span class=\"screen-reader-text\">Quadrat einer differenz (oder subtraktion)<\/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-332","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>Quadrat einer Differenz (oder Subtraktion) \u2013 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\/quadrat-einer-differenz-oder-subtraktion\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quadrat einer Differenz (oder Subtraktion) \u2013 Mathematik\" \/>\n<meta property=\"og:description\" content=\"Hier erkl\u00e4ren wir, was die bemerkenswerte Identit\u00e4tsformel des Quadrats einer Differenz (oder Subtraktion) ist, das hei\u00dft, wir zeigen Ihnen, wie der Ausdruck (ab) 2 gel\u00f6st wird. Dar\u00fcber hinaus k\u00f6nnen Sie Beispiele sehen und mit \u00dcbungen \u00fcben, die zum Quadrat der Differenz gel\u00f6st werden. 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