展开-((x+1)(x-2)(x-5))/8

解答

展开

- \frac{( x + 1 ) ( x - 2 ) ( x - 5 )}{8}

- \frac{x ^{3}}{8} + \frac{3 x ^{2}}{4} - \frac{3 x}{8} - \frac{5}{4}

求解步骤

- \frac{( x + 1 ) ( x - 2 ) ( x - 5 )}{8}

乘开

(x + 1) (x - 2) (x - 5) : x^{3} - 6 x^{2} + 3 x + 10

= - \frac{x ^{3} - 6 x ^{2} + 3 x + 10}{8}

使用分式法则:

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

\frac{x ^{3} - 6 x ^{2} + 3 x + 10}{8} = - (\frac{x ^{3}}{8}) - (- \frac{6 x ^{2}}{8}) - (\frac{3 x}{8}) - (\frac{10}{8})

= - (\frac{x ^{3}}{8}) - (- \frac{6 x ^{2}}{8}) - (\frac{3 x}{8}) - (\frac{10}{8})

去除括号:

(a) = a, - (- a) = a

= - \frac{x ^{3}}{8} + \frac{6 x ^{2}}{8} - \frac{3 x}{8} - \frac{10}{8}

消掉

\frac{6 x ^{2}}{8} : \frac{3 x ^{2}}{4}

= - \frac{x ^{3}}{8} + \frac{3 x ^{2}}{4} - \frac{3 x}{8} - \frac{10}{8}

消掉

\frac{10}{8} : \frac{5}{4}

= - \frac{x ^{3}}{8} + \frac{3 x ^{2}}{4} - \frac{3 x}{8} - \frac{5}{4}

e x p an d 3 x - 2 \cdot (3 x - 2)

e x p an d x^{2} + 3 x - 28 x^{2} + 3 x - 28

e x p an d \frac{4 s ^{3} + 4 + 2 e ^{- s} s ^{2}}{s ^{2} ( s ^{2} - 4 s + 3 )}

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

s im pl i f y 5 (75 + 21397)