展开 ((-z-1)^2z^2)/4

解答

展开

\frac{( - z - 1 ) ^{2} z ^{2}}{4}

\frac{z ^{4}}{4} + \frac{z ^{3}}{2} + \frac{z ^{2}}{4}

求解步骤

\frac{( - z - 1 ) ^{2} z ^{2}}{4}

(- z - 1)^{2} = z^{2} + 2 z + 1

= \frac{z ^{2} ( z ^{2} + 2 z + 1 )}{4}

乘开

(z^{2} + 2 z + 1) z^{2} : z^{4} + 2 z^{3} + z^{2}

= \frac{z ^{4} + 2 z ^{3} + z ^{2}}{4}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{z ^{4} + 2 z ^{3} + z ^{2}}{4} = \frac{z ^{4}}{4} + \frac{2 z ^{3}}{4} + \frac{z ^{2}}{4}

= \frac{z ^{4}}{4} + \frac{2 z ^{3}}{4} + \frac{z ^{2}}{4}

消掉

\frac{2 z ^{3}}{4} : \frac{z ^{3}}{2}

= \frac{z ^{4}}{4} + \frac{z ^{3}}{2} + \frac{z ^{2}}{4}

e x p an d 5 (e - 4)

\frac{\partial}{\partial x} ((z) (x sin (x y) - z))

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

e x p an d \frac{1}{s ( s ^{2} + 3 s + 5 )}

e x p an d \frac{x ^{2} ( - 10 x ^{3} + 3 x ^{2} - 60 x )}{20}