展开 (4(3-x)^4)/(81)

解答

展开

\frac{4 ( 3 - x ) ^{4}}{81}

\frac{4 x ^{4}}{81} - \frac{16 x ^{3}}{27} + \frac{8 x ^{2}}{3} - \frac{16 x}{3} + 4

求解步骤

\frac{4 ( 3 - x ) ^{4}}{81}

(3 - x)^{4} = 81 - 108 x + 54 x^{2} - 12 x^{3} + x^{4}

= \frac{4 ( x ^{4} - 12 x ^{3} + 54 x ^{2} - 108 x + 81 )}{81}

乘开

4 (81 - 108 x + 54 x^{2} - 12 x^{3} + x^{4}) : 324 - 432 x + 216 x^{2} - 48 x^{3} + 4 x^{4}

= \frac{324 - 432 x + 216 x ^{2} - 48 x ^{3} + 4 x ^{4}}{81}

使用分式法则:

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

\frac{324 - 432 x + 216 x ^{2} - 48 x ^{3} + 4 x ^{4}}{81} = \frac{324}{81} - \frac{432 x}{81} + \frac{216 x ^{2}}{81} - \frac{48 x ^{3}}{81} + \frac{4 x ^{4}}{81}

= \frac{324}{81} - \frac{432 x}{81} + \frac{216 x ^{2}}{81} - \frac{48 x ^{3}}{81} + \frac{4 x ^{4}}{81}

\frac{324}{81} = 4

\frac{432 x}{81} = \frac{16 x}{3}

\frac{216 x ^{2}}{81} = \frac{8 x ^{2}}{3}

\frac{48 x ^{3}}{81} = \frac{16 x ^{3}}{27}

= 4 - \frac{16 x}{3} + \frac{8 x ^{2}}{3} - \frac{16 x ^{3}}{27} + \frac{4 x ^{4}}{81}

改写为标准形式

= \frac{4 x ^{4}}{81} - \frac{16 x ^{3}}{27} + \frac{8 x ^{2}}{3} - \frac{16 x}{3} + 4

e x p an d \frac{( x \cdot e ^{x} )}{( ( x + 1 ) ^{2} )}

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

e x p an d 2 (ln (2 x) + b)

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

e x p an d \frac{\partial}{\partial x} ((x - a)^{2}) + (y - b)^{2}