展开 ((8x-3)^3)/(1728)

解答

展开

\frac{( 8 x - 3 ) ^{3}}{1728}

\frac{8 x ^{3}}{27} - \frac{x ^{2}}{3} + \frac{x}{8} - \frac{1}{64}

求解步骤

\frac{( 8 x - 3 ) ^{3}}{1728}

(8 x - 3)^{3} = 512 x^{3} - 576 x^{2} + 216 x - 27

= \frac{512 x ^{3} - 576 x ^{2} + 216 x - 27}{1728}

使用分式法则:

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

\frac{512 x ^{3} - 576 x ^{2} + 216 x - 27}{1728} = \frac{512 x ^{3}}{1728} - \frac{576 x ^{2}}{1728} + \frac{216 x}{1728} - \frac{27}{1728}

= \frac{512 x ^{3}}{1728} - \frac{576 x ^{2}}{1728} + \frac{216 x}{1728} - \frac{27}{1728}

\frac{512 x ^{3}}{1728} = \frac{8 x ^{3}}{27}

\frac{576 x ^{2}}{1728} = \frac{x ^{2}}{3}

\frac{216 x}{1728} = \frac{x}{8}

\frac{27}{1728} = \frac{1}{64}

= \frac{8 x ^{3}}{27} - \frac{x ^{2}}{3} + \frac{x}{8} - \frac{1}{64}

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