展開する (1+x-2x^2)^6

解

展開する

(1 + x - 2 x^{2})^{6}

64 x^{12} - 192 x^{11} + 48 x^{10} + 320 x^{9} - 180 x^{8} - 252 x^{7} + 141 x^{6} + 126 x^{5} - 45 x^{4} - 40 x^{3} + 3 x^{2} + 6 x + 1

解答ステップ

(1 + x - 2 x^{2})^{6}

(1 + x - 2 x^{2})^{6} = (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2})

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

拡張

(1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) : 64 x^{12} - 192 x^{11} + 48 x^{10} + 320 x^{9} - 180 x^{8} - 252 x^{7} + 141 x^{6} + 126 x^{5} - 45 x^{4} - 40 x^{3} + 3 x^{2} + 6 x + 1

= 64 x^{12} - 192 x^{11} + 48 x^{10} + 320 x^{9} - 180 x^{8} - 252 x^{7} + 141 x^{6} + 126 x^{5} - 45 x^{4} - 40 x^{3} + 3 x^{2} + 6 x + 1