展開する (x^2-x+4)^8

解

展開する

(x^{2} - x + 4)^{8}

x^{16} - 8 x^{15} + 60 x^{14} - 280 x^{13} + 1190 x^{12} - 3864 x^{11} + 11452 x^{10} - 27560 x^{9} + 60705 x^{8} - 110240 x^{7} + 183232 x^{6} - 247296 x^{5} + 304640 x^{4} - 286720 x^{3} + 245760 x^{2} - 131072 x + 65536

解答ステップ

(x^{2} - x + 4)^{8}

(x^{2} - x + 4)^{8} = (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) (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^{2} - x + 4) (x^{2} - x + 4) : x^{16} - 8 x^{15} + 60 x^{14} - 280 x^{13} + 1190 x^{12} - 3864 x^{11} + 11452 x^{10} - 27560 x^{9} + 60705 x^{8} - 110240 x^{7} + 183232 x^{6} - 247296 x^{5} + 304640 x^{4} - 286720 x^{3} + 245760 x^{2} - 131072 x + 65536

= x^{16} - 8 x^{15} + 60 x^{14} - 280 x^{13} + 1190 x^{12} - 3864 x^{11} + 11452 x^{10} - 27560 x^{9} + 60705 x^{8} - 110240 x^{7} + 183232 x^{6} - 247296 x^{5} + 304640 x^{4} - 286720 x^{3} + 245760 x^{2} - 131072 x + 65536