展開する (3x^4-2x^2+1)^5

解

展開する

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

243 x^{20} - 810 x^{18} + 1485 x^{16} - 1800 x^{14} + 1590 x^{12} - 1052 x^{10} + 530 x^{8} - 200 x^{6} + 55 x^{4} - 10 x^{2} + 1

解答ステップ

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

(3 x^{4} - 2 x^{2} + 1)^{5} = (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1)

= (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1)

拡張

(3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) (3 x^{4} - 2 x^{2} + 1) : 243 x^{20} - 810 x^{18} + 1485 x^{16} - 1800 x^{14} + 1590 x^{12} - 1052 x^{10} + 530 x^{8} - 200 x^{6} + 55 x^{4} - 10 x^{2} + 1

= 243 x^{20} - 810 x^{18} + 1485 x^{16} - 1800 x^{14} + 1590 x^{12} - 1052 x^{10} + 530 x^{8} - 200 x^{6} + 55 x^{4} - 10 x^{2} + 1