展开 (1+3x^2-2x^4)^6

解答

展开

(1 + 3 x^{2} - 2 x^{4})^{6}

64 x^{24} - 576 x^{22} + 1968 x^{20} - 2880 x^{18} + 780 x^{16} + 2124 x^{14} - 1051 x^{12} - 1062 x^{10} + 195 x^{8} + 360 x^{6} + 123 x^{4} + 18 x^{2} + 1

求解步骤

(1 + 3 x^{2} - 2 x^{4})^{6}

(1 + 3 x^{2} - 2 x^{4})^{6} = (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4})

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

乘开

(1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) (1 + 3 x^{2} - 2 x^{4}) : 64 x^{24} - 576 x^{22} + 1968 x^{20} - 2880 x^{18} + 780 x^{16} + 2124 x^{14} - 1051 x^{12} - 1062 x^{10} + 195 x^{8} + 360 x^{6} + 123 x^{4} + 18 x^{2} + 1

= 64 x^{24} - 576 x^{22} + 1968 x^{20} - 2880 x^{18} + 780 x^{16} + 2124 x^{14} - 1051 x^{12} - 1062 x^{10} + 195 x^{8} + 360 x^{6} + 123 x^{4} + 18 x^{2} + 1

e x p an d \frac{x ( x - 10 )}{2}

e x p an d - \frac{4}{( x - 3 ) ^{2}}

e x p an d t e^{t} (2 t + 4)

e x p an d \frac{10 - x}{x ( x ^{2} - 4 x + 1 )}

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