展开 (x((x-3)^2))/9

解答

展开

\frac{x ( ( x - 3 ) ^{2} )}{9}

\frac{x ^{3}}{9} - \frac{2 x ^{2}}{3} + x

求解步骤

\frac{x ( ( x - 3 ) ^{2} )}{9}

去除括号:

(a) = a

= \frac{x ( x - 3 ) ^{2}}{9}

(x - 3)^{2} = x^{2} - 6 x + 9

= \frac{x ( x ^{2} - 6 x + 9 )}{9}

乘开

x (x^{2} - 6 x + 9) : x^{3} - 6 x^{2} + 9 x

= \frac{x ^{3} - 6 x ^{2} + 9 x}{9}

使用分式法则:

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

\frac{x ^{3} - 6 x ^{2} + 9 x}{9} = \frac{x ^{3}}{9} - \frac{6 x ^{2}}{9} + \frac{9 x}{9}

= \frac{x ^{3}}{9} - \frac{6 x ^{2}}{9} + \frac{9 x}{9}

消掉

\frac{6 x ^{2}}{9} : \frac{2 x ^{2}}{3}

= \frac{x ^{3}}{9} - \frac{2 x ^{2}}{3} + \frac{9 x}{9}

数字相除:

\frac{9}{9} = 1

= \frac{x ^{3}}{9} - \frac{2 x ^{2}}{3} + x

e x p an d (1 - e^{- 3 x})^{2}

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

\frac{d}{d y} ((x) (x^{3} + 3 y^{3} + 5 x + y))

s im pl i f y e^{- s t} \cdot t \cdot (e^{i t} + e^{- i t})

e x p an d 2 π (\frac{9 π}{4} - 36)