展開する (10x^4-11x^2+1)^5

解

展開する

(10 x^{4} - 11 x^{2} + 1)^{5}

100000 x^{20} - 550000 x^{18} + 1260000 x^{16} - 1551000 x^{14} + 1105050 x^{12} - 460251 x^{10} + 110505 x^{8} - 15510 x^{6} + 1260 x^{4} - 55 x^{2} + 1

解答ステップ

(10 x^{4} - 11 x^{2} + 1)^{5}

(10 x^{4} - 11 x^{2} + 1)^{5} = (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1)

= (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1)

拡張

(10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) (10 x^{4} - 11 x^{2} + 1) : 100000 x^{20} - 550000 x^{18} + 1260000 x^{16} - 1551000 x^{14} + 1105050 x^{12} - 460251 x^{10} + 110505 x^{8} - 15510 x^{6} + 1260 x^{4} - 55 x^{2} + 1

= 100000 x^{20} - 550000 x^{18} + 1260000 x^{16} - 1551000 x^{14} + 1105050 x^{12} - 460251 x^{10} + 110505 x^{8} - 15510 x^{6} + 1260 x^{4} - 55 x^{2} + 1