展開する (4-x+x^2)^5

解

展開する

(4 - x + x^{2})^{5}

x^{10} - 5 x^{9} + 30 x^{8} - 90 x^{7} + 285 x^{6} - 561 x^{5} + 1140 x^{4} - 1440 x^{3} + 1920 x^{2} - 1280 x + 1024

解答ステップ

(4 - x + x^{2})^{5}

(4 - x + x^{2})^{5} = (4 - x + x^{2}) (4 - x + x^{2}) (4 - x + x^{2}) (4 - x + x^{2}) (4 - x + x^{2})

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

拡張

(4 - x + x^{2}) (4 - x + x^{2}) (4 - x + x^{2}) (4 - x + x^{2}) (4 - x + x^{2}) : x^{10} - 5 x^{9} + 30 x^{8} - 90 x^{7} + 285 x^{6} - 561 x^{5} + 1140 x^{4} - 1440 x^{3} + 1920 x^{2} - 1280 x + 1024

= x^{10} - 5 x^{9} + 30 x^{8} - 90 x^{7} + 285 x^{6} - 561 x^{5} + 1140 x^{4} - 1440 x^{3} + 1920 x^{2} - 1280 x + 1024