展開する (x^2-x+4)^6

解

展開する

(x^{2} - x + 4)^{6}

x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 495 x^{8} - 1206 x^{7} + 2841 x^{6} - 4824 x^{5} + 7920 x^{4} - 8960 x^{3} + 9984 x^{2} - 6144 x + 4096

解答ステップ

(x^{2} - x + 4)^{6}

(x^{2} - x + 4)^{6} = (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4)

= (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4)

拡張

(x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) : x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 495 x^{8} - 1206 x^{7} + 2841 x^{6} - 4824 x^{5} + 7920 x^{4} - 8960 x^{3} + 9984 x^{2} - 6144 x + 4096

= x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 495 x^{8} - 1206 x^{7} + 2841 x^{6} - 4824 x^{5} + 7920 x^{4} - 8960 x^{3} + 9984 x^{2} - 6144 x + 4096