展开 (((x+1)(x)(x-2))/(-2))*3

解答

展开

(\frac{( x + 1 ) ( x ) ( x - 2 )}{- 2}) \cdot 3

- \frac{3 x ^{3}}{2} + \frac{3 x ^{2}}{2} + 3 x

求解步骤

(\frac{( x + 1 ) ( x ) ( x - 2 )}{- 2}) \cdot 3

去除括号:

(a) = a

= \frac{( x + 1 ) x ( x - 2 )}{- 2} \cdot 3

\frac{( x + 1 ) x ( x - 2 )}{- 2} = - \frac{x ^{3} - x ^{2} - 2 x}{2}

= - 3 \cdot \frac{x ^{3} - x ^{2} - 2 x}{2}

分式相乘:

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

= - \frac{( x ^{3} - x ^{2} - 2 x ) \cdot 3}{2}

乘开

(x^{3} - x^{2} - 2 x) \cdot 3 : 3 x^{3} - 3 x^{2} - 6 x

= - \frac{3 x ^{3} - 3 x ^{2} - 6 x}{2}

使用分式法则:

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

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

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

去除括号:

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

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

数字相除:

\frac{6}{2} = 3

= - \frac{3 x ^{3}}{2} + \frac{3 x ^{2}}{2} + 3 x

e x p an d \frac{9 ( x ^{10} - 1 )}{5}

e x p an d \frac{10 x ^{2} + 10}{( x + 1 ) ^{4}}

e x p an d \frac{x ( 128 x ^{2} - 735 x - 264 )}{64 ( x - 4 ) ^{2}}

e x p an d \frac{8 ( s + 3 )}{( s + 8 ) ( s ^{2} + 24 s + 135 )}

e x p an d \frac{11 x ^{2} - 2 x + 2}{x ( 3 x ^{2} + 1 )}