展开 ((((x^3-2x)^5)))/5

解答

展开

\frac{( ( ( x ^{3} - 2 x ) ^{5} ) )}{5}

\frac{x ^{15}}{5} - 2 x^{13} + 8 x^{11} - 16 x^{9} + 16 x^{7} - \frac{32 x ^{5}}{5}

求解步骤

\frac{( x ^{3} - 2 x ) ^{5}}{5}

(x^{3} - 2 x)^{5} = x^{15} - 10 x^{13} + 40 x^{11} - 80 x^{9} + 80 x^{7} - 32 x^{5}

= \frac{x ^{15} - 10 x ^{13} + 40 x ^{11} - 80 x ^{9} + 80 x ^{7} - 32 x ^{5}}{5}

使用分式法则:

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

\frac{x ^{15} - 10 x ^{13} + 40 x ^{11} - 80 x ^{9} + 80 x ^{7} - 32 x ^{5}}{5} = \frac{x ^{15}}{5} - \frac{10 x ^{13}}{5} + \frac{40 x ^{11}}{5} - \frac{80 x ^{9}}{5} + \frac{80 x ^{7}}{5} - \frac{32 x ^{5}}{5}

= \frac{x ^{15}}{5} - \frac{10 x ^{13}}{5} + \frac{40 x ^{11}}{5} - \frac{80 x ^{9}}{5} + \frac{80 x ^{7}}{5} - \frac{32 x ^{5}}{5}

\frac{10 x ^{13}}{5} = 2 x^{13}

\frac{40 x ^{11}}{5} = 8 x^{11}

\frac{80 x ^{9}}{5} = 16 x^{9}

\frac{80 x ^{7}}{5} = 16 x^{7}

= \frac{x ^{15}}{5} - 2 x^{13} + 8 x^{11} - 16 x^{9} + 16 x^{7} - \frac{32 x ^{5}}{5}

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