展开 (((x-2)^5))/5

解答

展开

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

\frac{x ^{5}}{5} - 2 x^{4} + 8 x^{3} - 16 x^{2} + 16 x - \frac{32}{5}

求解步骤

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

(x - 2)^{5} = x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 80 x - 32

= \frac{x ^{5} - 10 x ^{4} + 40 x ^{3} - 80 x ^{2} + 80 x - 32}{5}

使用分式法则:

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

\frac{x ^{5} - 10 x ^{4} + 40 x ^{3} - 80 x ^{2} + 80 x - 32}{5} = \frac{x ^{5}}{5} - \frac{10 x ^{4}}{5} + \frac{40 x ^{3}}{5} - \frac{80 x ^{2}}{5} + \frac{80 x}{5} - \frac{32}{5}

= \frac{x ^{5}}{5} - \frac{10 x ^{4}}{5} + \frac{40 x ^{3}}{5} - \frac{80 x ^{2}}{5} + \frac{80 x}{5} - \frac{32}{5}

\frac{10 x ^{4}}{5} = 2 x^{4}

\frac{40 x ^{3}}{5} = 8 x^{3}

\frac{80 x ^{2}}{5} = 16 x^{2}

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

= \frac{x ^{5}}{5} - 2 x^{4} + 8 x^{3} - 16 x^{2} + 16 x - \frac{32}{5}

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