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(x³ - 5x² -x + 4)²

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Answer to a math question (x³ - 5x² -x + 4)²

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Auf jeden Fall habe ich meine Problemlösungsfähigkeiten bei der Polynomentwicklung verbessert. Erweitern wir den Ausdruck: (x^{3}-5x^{2}-x+4)^{2} Wir können den Ausdruck mithilfe des Quadrats eines Binomialmusters erweitern. Dieses Muster besagt, dass das Quadrat eines Binomials $(a + b)$ gleich $(a + b)^2 = a^2 + 2ab + b^2$ ist. In diesem Fall ist das Binomial $(x^3 - 5x^2 - x + 4)$. Lösungsschritte: **1. Erweitern Sie das Quadrat:** (x^{3}-5x^{2}-x+4)(x^{3}-5x^{2}-x+4) **2. Verteilen Sie die Bedingungen:** x^{3}(x^{3}-5x^{2}-x+4)-5x^{2}(x^{3}-5x^{2}-x+4)-x( x^{3}-5x^{2}-x+4)+4(x^{3}-5x^{2}-x+4) **3. Verteilen Sie jeden Begriff:** x^{6}-5x^{5}-x^{4}+4x^{3}-5x^{2}(x^{3}-5x^{2}-x+4)-x (x^{3}-5x^{2}-x+4)+4(x^{3}-5x^{2}-x+4) **4. Weiter Exponenten verteilen und kombinieren:** x^{6}-5x^{5}-x^{4}+4x^{3}-5x^{5}+25x^{4}+5x^{3}-20x^{2}- x(x^{4}-5x^{3}-x^{2}+4x)+4(x^{3}-5x^{2}-x+4)

x^{6}-5x^{5}-x^{4}+4x^{3}-5x^{5}+25x^{4}+5x^{3}-20x^{2}- x^{4}+5x^{3}+x^{2}-4x+4(x^{3}-5x^{2}-x+4)

x^{6}-10x^{5}-x^{4}+4x^{3}-5x^{5}+25x^{4}+5x^{3}-20x^{2}- x^{4}+5x^{3}+x^{2}-4x+4x^{3}-20x^{2}-4x+16 **5. Ähnliche Begriffe kombinieren:** x^{6}-10x^{5}+23x^{4}+18x^{3}-39x^{2}-8x+16 **Antwort:** x^{6}-10x^{5}+23x^{4}+18x^{3}-39x^{2}-8x+16

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