展開する (1-3x+x^2)^8

解

展開する

(1 - 3 x + x^{2})^{8}

x^{16} - 24 x^{15} + 260 x^{14} - 1680 x^{13} + 7210 x^{12} - 21672 x^{11} + 46928 x^{10} - 74280 x^{9} + 86515 x^{8} - 74280 x^{7} + 46928 x^{6} - 21672 x^{5} + 7210 x^{4} - 1680 x^{3} + 260 x^{2} - 24 x + 1

解答ステップ

(1 - 3 x + x^{2})^{8}

(1 - 3 x + x^{2})^{8} = (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2})

= (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1)

拡張

(1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) : x^{16} - 24 x^{15} + 260 x^{14} - 1680 x^{13} + 7210 x^{12} - 21672 x^{11} + 46928 x^{10} - 74280 x^{9} + 86515 x^{8} - 74280 x^{7} + 46928 x^{6} - 21672 x^{5} + 7210 x^{4} - 1680 x^{3} + 260 x^{2} - 24 x + 1

= x^{16} - 24 x^{15} + 260 x^{14} - 1680 x^{13} + 7210 x^{12} - 21672 x^{11} + 46928 x^{10} - 74280 x^{9} + 86515 x^{8} - 74280 x^{7} + 46928 x^{6} - 21672 x^{5} + 7210 x^{4} - 1680 x^{3} + 260 x^{2} - 24 x + 1