展开 ((-3x^2y+1)^3)/(27x^8)

解答

展开

\frac{( - 3 x ^{2} y + 1 ) ^{3}}{27 x ^{8}}

- \frac{y ^{3}}{x ^{2}} + \frac{y ^{2}}{x ^{4}} - \frac{y}{3 x ^{6}} + \frac{1}{27 x ^{8}}

求解步骤

\frac{( - 3 x ^{2} y + 1 ) ^{3}}{27 x ^{8}}

(- 3 x^{2} y + 1)^{3} = - 27 x^{6} y^{3} + 27 x^{4} y^{2} - 9 x^{2} y + 1

= \frac{( - 27 x ^{6} y ^{3} + 27 x ^{4} y ^{2} - 9 x ^{2} y + 1 )}{27 x ^{8}}

去除括号:

(- a) = - a

= \frac{- 27 x ^{6} y ^{3} + 27 x ^{4} y ^{2} - 9 x ^{2} y + 1}{27 x ^{8}}

使用分式法则:

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

\frac{- 27 x ^{6} y ^{3} + 27 x ^{4} y ^{2} - 9 x ^{2} y + 1}{27 x ^{8}} = - \frac{27 x ^{6} y ^{3}}{27 x ^{8}} + \frac{27 x ^{4} y ^{2}}{27 x ^{8}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

= - \frac{27 x ^{6} y ^{3}}{27 x ^{8}} + \frac{27 x ^{4} y ^{2}}{27 x ^{8}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

消掉

\frac{27 x ^{6} y ^{3}}{27 x ^{8}} : \frac{y ^{3}}{x ^{2}}

= - \frac{y ^{3}}{x ^{2}} + \frac{27 x ^{4} y ^{2}}{27 x ^{8}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

消掉

\frac{27 x ^{4} y ^{2}}{27 x ^{8}} : \frac{y ^{2}}{x ^{4}}

= - \frac{y ^{3}}{x ^{2}} + \frac{y ^{2}}{x ^{4}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

消掉

\frac{9 x ^{2} y}{27 x ^{8}} : \frac{y}{3 x ^{6}}

= - \frac{y ^{3}}{x ^{2}} + \frac{y ^{2}}{x ^{4}} - \frac{y}{3 x ^{6}} + \frac{1}{27 x ^{8}}

e x p an d \frac{1}{( s ^{2} + 1 ) ( s - 3 ) ( s - 6 )}

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

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

e x p an d (3 + 9 - k)^{3}

s im pl i f y (\frac{x}{y} - \frac{y}{z})^{2}