展开 (3x^4-2x^2+1)^5

解答

展开

(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

求解步骤

(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)

乘开

(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

e x p an d 40 (e^{- t} - e^{- 2 t})

e x p an d - 7 (3 x + 2 y = - 7)

e x p an d (2 y e^{x y} + x e^{x y})^{2}

s im pl i f y (1 + cos (x) + i sin (x))^{2}

e x p an d - 7 (5 x + 42 y = - 69)