展开 ((-24x^2+12x-15)(4x-1))/(16)

解答

展开

\frac{( - 24 x ^{2} + 12 x - 15 ) ( 4 x - 1 )}{16}

- 6 x^{3} + \frac{9 x ^{2}}{2} - \frac{9 x}{2} + \frac{15}{16}

求解步骤

\frac{( - 24 x ^{2} + 12 x - 15 ) ( 4 x - 1 )}{16}

乘开

(- 24 x^{2} + 12 x - 15) (4 x - 1) : - 96 x^{3} + 72 x^{2} - 72 x + 15

= \frac{- 96 x ^{3} + 72 x ^{2} - 72 x + 15}{16}

使用分式法则:

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

\frac{- 96 x ^{3} + 72 x ^{2} - 72 x + 15}{16} = - \frac{96 x ^{3}}{16} + \frac{72 x ^{2}}{16} - \frac{72 x}{16} + \frac{15}{16}

= - \frac{96 x ^{3}}{16} + \frac{72 x ^{2}}{16} - \frac{72 x}{16} + \frac{15}{16}

数字相除:

\frac{96}{16} = 6

= - 6 x^{3} + \frac{72 x ^{2}}{16} - \frac{72 x}{16} + \frac{15}{16}

消掉

\frac{72 x ^{2}}{16} : \frac{9 x ^{2}}{2}

= - 6 x^{3} + \frac{9 x ^{2}}{2} - \frac{72 x}{16} + \frac{15}{16}

消掉

\frac{72 x}{16} : \frac{9 x}{2}

= - 6 x^{3} + \frac{9 x ^{2}}{2} - \frac{9 x}{2} + \frac{15}{16}

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