展开-(x^2(-10x^3+3x^2-60x))/(20)

解答

展开

- \frac{x ^{2} ( - 10 x ^{3} + 3 x ^{2} - 60 x )}{20}

\frac{x ^{5}}{2} - \frac{3 x ^{4}}{20} + 3 x^{3}

求解步骤

- \frac{x ^{2} ( - 10 x ^{3} + 3 x ^{2} - 60 x )}{20}

乘开

x^{2} (- 10 x^{3} + 3 x^{2} - 60 x) : - 10 x^{5} + 3 x^{4} - 60 x^{3}

= - \frac{- 10 x ^{5} + 3 x ^{4} - 60 x ^{3}}{20}

使用分式法则:

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

\frac{- 10 x ^{5} + 3 x ^{4} - 60 x ^{3}}{20} = - (- \frac{10 x ^{5}}{20}) - (\frac{3 x ^{4}}{20}) - (- \frac{60 x ^{3}}{20})

= - (- \frac{10 x ^{5}}{20}) - (\frac{3 x ^{4}}{20}) - (- \frac{60 x ^{3}}{20})

去除括号:

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

= \frac{10 x ^{5}}{20} - \frac{3 x ^{4}}{20} + \frac{60 x ^{3}}{20}

消掉

\frac{10 x ^{5}}{20} : \frac{x ^{5}}{2}

= \frac{x ^{5}}{2} - \frac{3 x ^{4}}{20} + \frac{60 x ^{3}}{20}

数字相除:

\frac{60}{20} = 3

= \frac{x ^{5}}{2} - \frac{3 x ^{4}}{20} + 3 x^{3}

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