展開する (1-2x+x^2)^5

解

展開する

(1 - 2 x + x^{2})^{5}

x^{10} - 10 x^{9} + 45 x^{8} - 120 x^{7} + 210 x^{6} - 252 x^{5} + 210 x^{4} - 120 x^{3} + 45 x^{2} - 10 x + 1

解答ステップ

(1 - 2 x + x^{2})^{5}

(1 - 2 x + x^{2})^{5} = (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2})

= (x^{2} - 2 x + 1) (x^{2} - 2 x + 1) (x^{2} - 2 x + 1) (x^{2} - 2 x + 1) (x^{2} - 2 x + 1)

拡張

(1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) : x^{10} - 10 x^{9} + 45 x^{8} - 120 x^{7} + 210 x^{6} - 252 x^{5} + 210 x^{4} - 120 x^{3} + 45 x^{2} - 10 x + 1

= x^{10} - 10 x^{9} + 45 x^{8} - 120 x^{7} + 210 x^{6} - 252 x^{5} + 210 x^{4} - 120 x^{3} + 45 x^{2} - 10 x + 1