erweitern (a+bx+cx^2+dx^3+ex^4)^2

Lösung

erweitern

(a + b x + c x^{2} + d x^{3} + e x^{4})^{2}

e^{2} x^{8} + 2 e a x^{4} + 2 e b x^{5} + 2 ec x^{6} + 2 e d x^{7} + 2 a d x^{3} + 2 b d x^{4} + 2 c d x^{5} + d^{2} x^{6} + 2 a c x^{2} + 2 b c x^{3} + c^{2} x^{4} + 2 ab x + b^{2} x^{2} + a^{2}

Schritte zur Lösung

(a + b x + c x^{2} + d x^{3} + e x^{4})^{2}

(a + b x + c x^{2} + d x^{3} + e x^{4})^{2} = (a + b x + c x^{2} + d x^{3} + e x^{4}) (a + b x + c x^{2} + d x^{3} + e x^{4})

= (e x^{4} + d x^{3} + c x^{2} + b x + a) (e x^{4} + d x^{3} + c x^{2} + b x + a)

Multipliziere aus

(a + b x + c x^{2} + d x^{3} + e x^{4}) (a + b x + c x^{2} + d x^{3} + e x^{4}) : e^{2} x^{8} + 2 e a x^{4} + 2 e b x^{5} + 2 ec x^{6} + 2 e d x^{7} + 2 a d x^{3} + 2 b d x^{4} + 2 c d x^{5} + d^{2} x^{6} + 2 a c x^{2} + 2 b c x^{3} + c^{2} x^{4} + 2 ab x + b^{2} x^{2} + a^{2}

= e^{2} x^{8} + 2 e a x^{4} + 2 e b x^{5} + 2 ec x^{6} + 2 e d x^{7} + 2 a d x^{3} + 2 b d x^{4} + 2 c d x^{5} + d^{2} x^{6} + 2 a c x^{2} + 2 b c x^{3} + c^{2} x^{4} + 2 ab x + b^{2} x^{2} + a^{2}

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e x p an d - \frac{2 x ( - 2 x + 6 ) ^{3}}{81}

e x p an d (4 t + 1) H (t - 1)

e x p an d 5 sin (\frac{π}{2} (x + 7)) - 8