展開する (2+x-x^2)^6

解

展開する

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

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

解答ステップ

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

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

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

拡張

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

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