展開する (1-x-x^2)^5

解

展開する

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

- x^{10} - 5 x^{9} - 5 x^{8} + 10 x^{7} + 15 x^{6} - 11 x^{5} - 15 x^{4} + 10 x^{3} + 5 x^{2} - 5 x + 1

解答ステップ

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

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

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

拡張

(1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) : - x^{10} - 5 x^{9} - 5 x^{8} + 10 x^{7} + 15 x^{6} - 11 x^{5} - 15 x^{4} + 10 x^{3} + 5 x^{2} - 5 x + 1

= - x^{10} - 5 x^{9} - 5 x^{8} + 10 x^{7} + 15 x^{6} - 11 x^{5} - 15 x^{4} + 10 x^{3} + 5 x^{2} - 5 x + 1