展开 (2(1-x^{3/2})^2)/3

解答

展开

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

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

求解步骤

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

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

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

乘开

2 (1 - 2 x^{\frac{3}{2}} + x^{3}) : 2 - 4 x^{\frac{3}{2}} + 2 x^{3}

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

使用分式法则:

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

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

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

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