展開する (1-w-w^2)^5

解

展開する

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

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

解答ステップ

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

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

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

拡張

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

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