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受欢迎的代数 >

展开-(2x(-2x+6)^3)/(81)

解答

展开

- \frac{2 x ( - 2 x + 6 ) ^{3}}{81}

解答

\frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{16 x ^{2}}{3} - \frac{16 x}{3}

求解步骤

- \frac{2 x ( - 2 x + 6 ) ^{3}}{81}

(- 2 x + 6)^{3} = - 8 x^{3} + 72 x^{2} - 216 x + 216

= - \frac{2 x ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{81}

乘开

2 x (- 8 x^{3} + 72 x^{2} - 216 x + 216) : - 16 x^{4} + 144 x^{3} - 432 x^{2} + 432 x

= - \frac{- 16 x ^{4} + 144 x ^{3} - 432 x ^{2} + 432 x}{81}

使用分式法则:

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

\frac{- 16 x ^{4} + 144 x ^{3} - 432 x ^{2} + 432 x}{81} = - (- \frac{16 x ^{4}}{81}) - (\frac{144 x ^{3}}{81}) - (- \frac{432 x ^{2}}{81}) - (\frac{432 x}{81})

= - (- \frac{16 x ^{4}}{81}) - (\frac{144 x ^{3}}{81}) - (- \frac{432 x ^{2}}{81}) - (\frac{432 x}{81})

去除括号:

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

= \frac{16 x ^{4}}{81} - \frac{144 x ^{3}}{81} + \frac{432 x ^{2}}{81} - \frac{432 x}{81}

消掉

\frac{144 x ^{3}}{81} : \frac{16 x ^{3}}{9}

= \frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{432 x ^{2}}{81} - \frac{432 x}{81}

消掉

\frac{432 x ^{2}}{81} : \frac{16 x ^{2}}{3}

= \frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{16 x ^{2}}{3} - \frac{432 x}{81}

消掉

\frac{432 x}{81} : \frac{16 x}{3}

= \frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{16 x ^{2}}{3} - \frac{16 x}{3}

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