展开 ((2-x)(x-3)(x-4))/(24)

解答

展开

\frac{( 2 - x ) ( x - 3 ) ( x - 4 )}{24}

- \frac{x ^{3}}{24} + \frac{3 x ^{2}}{8} - \frac{13 x}{12} + 1

求解步骤

\frac{( 2 - x ) ( x - 3 ) ( x - 4 )}{24}

乘开

(2 - x) (x - 3) (x - 4) : - x^{3} + 9 x^{2} - 26 x + 24

= \frac{- x ^{3} + 9 x ^{2} - 26 x + 24}{24}

使用分式法则:

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

\frac{- x ^{3} + 9 x ^{2} - 26 x + 24}{24} = - \frac{x ^{3}}{24} + \frac{9 x ^{2}}{24} - \frac{26 x}{24} + \frac{24}{24}

= - \frac{x ^{3}}{24} + \frac{9 x ^{2}}{24} - \frac{26 x}{24} + \frac{24}{24}

使用法则

\frac{a}{a} = 1

\frac{24}{24} = 1

= - \frac{x ^{3}}{24} + \frac{9 x ^{2}}{24} - \frac{26 x}{24} + 1

消掉

\frac{9 x ^{2}}{24} : \frac{3 x ^{2}}{8}

= - \frac{x ^{3}}{24} + \frac{3 x ^{2}}{8} - \frac{26 x}{24} + 1

消掉

\frac{26 x}{24} : \frac{13 x}{12}

= - \frac{x ^{3}}{24} + \frac{3 x ^{2}}{8} - \frac{13 x}{12} + 1

s im pl i f y (5 + sin (t))^{2} + cos^{2} (t)

e x p an d \frac{378.7 ( s + 1 )}{s ^{4} + 30 s ^{3} + 100 s ^{2} - 200 s + 400}

e x p an d - \frac{43}{16 ( 4 w - 1 )}

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

\frac{\partial}{\partial t} ((x) (2 t^{3} - 6 t^{2}))