展开 (6x^4(-24x^6+25y^5))/(25y^9)

解答

展开

\frac{6 x ^{4} ( - 24 x ^{6} + 25 y ^{5} )}{25 y ^{9}}

- \frac{144 x ^{10}}{25 y ^{9}} + \frac{6 x ^{4}}{y ^{4}}

求解步骤

\frac{6 x ^{4} ( - 24 x ^{6} + 25 y ^{5} )}{25 y ^{9}}

乘开

6 x^{4} (- 24 x^{6} + 25 y^{5}) : - 144 x^{10} + 150 x^{4} y^{5}

= \frac{- 144 x ^{10} + 150 x ^{4} y ^{5}}{25 y ^{9}}

使用分式法则:

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

\frac{- 144 x ^{10} + 150 x ^{4} y ^{5}}{25 y ^{9}} = - \frac{144 x ^{10}}{25 y ^{9}} + \frac{150 x ^{4} y ^{5}}{25 y ^{9}}

= - \frac{144 x ^{10}}{25 y ^{9}} + \frac{150 x ^{4} y ^{5}}{25 y ^{9}}

消掉

\frac{150 x ^{4} y ^{5}}{25 y ^{9}} : \frac{6 x ^{4}}{y ^{4}}

= - \frac{144 x ^{10}}{25 y ^{9}} + \frac{6 x ^{4}}{y ^{4}}

s im pl i f y (x - 2) (x - 3) (x + 3)

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

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

e x p an d \frac{1}{2} H (t + \frac{π}{4}) sin (2 (t + \frac{π}{4})) + 2 sin (2 t)

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