展開する (a+bx+cx^2+dx^3+ex^4+fx^5)^2

解

展開する

(a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5})^{2}

2 a x^{5} f + 2 b x^{6} f + 2 c x^{7} f + 2 d x^{8} f + 2 e x^{9} f + x^{10} f^{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}

解答ステップ

(a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5})^{2}

= (a + b x + c x^{2} + d x^{3} + e x^{4} + x^{5} f)^{2}

(a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5})^{2} = (a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5}) (a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5})

= (x^{5} f + e x^{4} + d x^{3} + c x^{2} + b x + a) (x^{5} f + e x^{4} + d x^{3} + c x^{2} + b x + a)

拡張

(a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5}) (a + b x + c x^{2} + d x^{3} + e x^{4} + f x^{5}) : 2 a x^{5} f + 2 b x^{6} f + 2 c x^{7} f + 2 d x^{8} f + 2 e x^{9} f + x^{10} f^{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}

= 2 a x^{5} f + 2 b x^{6} f + 2 c x^{7} f + 2 d x^{8} f + 2 e x^{9} f + x^{10} f^{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}