展开 (4t(-3t^5+5t^4)+15(t^4-t^2))/(30)

解答

展开

\frac{4 t ( - 3 t ^{5} + 5 t ^{4} ) + 15 ( t ^{4} - t ^{2} )}{30}

- \frac{2 t ^{6}}{5} + \frac{2 t ^{5}}{3} + \frac{t ^{4}}{2} - \frac{t ^{2}}{2}

求解步骤

\frac{4 t ( - 3 t ^{5} + 5 t ^{4} ) + 15 ( t ^{4} - t ^{2} )}{30}

乘开

4 t (- 3 t^{5} + 5 t^{4}) + 15 (t^{4} - t^{2}) : - 12 t^{6} + 20 t^{5} + 15 t^{4} - 15 t^{2}

= \frac{- 12 t ^{6} + 20 t ^{5} + 15 t ^{4} - 15 t ^{2}}{30}

使用分式法则:

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

\frac{- 12 t ^{6} + 20 t ^{5} + 15 t ^{4} - 15 t ^{2}}{30} = - \frac{12 t ^{6}}{30} + \frac{20 t ^{5}}{30} + \frac{15 t ^{4}}{30} - \frac{15 t ^{2}}{30}

= - \frac{12 t ^{6}}{30} + \frac{20 t ^{5}}{30} + \frac{15 t ^{4}}{30} - \frac{15 t ^{2}}{30}

\frac{12 t ^{6}}{30} = \frac{2 t ^{6}}{5}

\frac{20 t ^{5}}{30} = \frac{2 t ^{5}}{3}

\frac{15 t ^{4}}{30} = \frac{t ^{4}}{2}

\frac{15 t ^{2}}{30} = \frac{t ^{2}}{2}

= - \frac{2 t ^{6}}{5} + \frac{2 t ^{5}}{3} + \frac{t ^{4}}{2} - \frac{t ^{2}}{2}

s im pl i f y ((\frac{241363447}{129092883})^{\frac{1}{10}} - 1) \cdot 100

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

s im pl i f y (x - 3) (x + 2) (x - \frac{2}{3}) (x + 1)

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

e x p an d (2 x y^{2} + 2 y) + (2 x^{2} y + 2 x) y^{'} (x)