展开 x(x^2-1)^3dz

解答

展开

x (x^{2} - 1)^{3} d z

x^{7} d z - 3 x^{5} d z + 3 x^{3} d z - x d z

求解步骤

x (x^{2} - 1)^{3} d z

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

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

打开括号

= x d z x^{6} + x d z (- 3 x^{4}) + x d z \cdot 3 x^{2} + x d z (- 1)

使用加减运算法则

+ (- a) = - a

= x^{6} x d z - 3 x^{4} x d z + 3 x^{2} x d z - 1 \cdot x d z

化简

x^{6} x d z - 3 x^{4} x d z + 3 x^{2} x d z - 1 \cdot x d z : x^{7} d z - 3 x^{5} d z + 3 x^{3} d z - x d z

= x^{7} d z - 3 x^{5} d z + 3 x^{3} d z - x d z

e x p an d (x + 2 π) (x - 2 π)

e x p an d 16 e^{4 x} \cdot (1 + e^{4 x})

e x p an d \frac{1}{( x + 3 ) ( x - 2 )}

e x p an d \frac{x ( 400 - x )}{400}

e x p an d \frac{( x ^{2} - 3 x + 5 ) ^{2}}{( x - 2 )}