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受欢迎的代数 >

展开-(x(x-24)(x^2-24x+152))/(1152)

解答

展开

- \frac{x ( x - 24 ) ( x ^{2} - 24 x + 152 )}{1152}

解答

- \frac{x ^{4}}{1152} + \frac{x ^{3}}{24} - \frac{91 x ^{2}}{144} + \frac{19 x}{6}

求解步骤

- \frac{x ( x - 24 ) ( x ^{2} - 24 x + 152 )}{1152}

乘开

x (x - 24) (x^{2} - 24 x + 152) : x^{4} - 48 x^{3} + 728 x^{2} - 3648 x

= - \frac{x ^{4} - 48 x ^{3} + 728 x ^{2} - 3648 x}{1152}

使用分式法则:

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

\frac{x ^{4} - 48 x ^{3} + 728 x ^{2} - 3648 x}{1152} = - (\frac{x ^{4}}{1152}) - (- \frac{48 x ^{3}}{1152}) - (\frac{728 x ^{2}}{1152}) - (- \frac{3648 x}{1152})

= - (\frac{x ^{4}}{1152}) - (- \frac{48 x ^{3}}{1152}) - (\frac{728 x ^{2}}{1152}) - (- \frac{3648 x}{1152})

去除括号:

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

= - \frac{x ^{4}}{1152} + \frac{48 x ^{3}}{1152} - \frac{728 x ^{2}}{1152} + \frac{3648 x}{1152}

消掉

\frac{48 x ^{3}}{1152} : \frac{x ^{3}}{24}

= - \frac{x ^{4}}{1152} + \frac{x ^{3}}{24} - \frac{728 x ^{2}}{1152} + \frac{3648 x}{1152}

消掉

\frac{728 x ^{2}}{1152} : \frac{91 x ^{2}}{144}

= - \frac{x ^{4}}{1152} + \frac{x ^{3}}{24} - \frac{91 x ^{2}}{144} + \frac{3648 x}{1152}

消掉

\frac{3648 x}{1152} : \frac{19 x}{6}

= - \frac{x ^{4}}{1152} + \frac{x ^{3}}{24} - \frac{91 x ^{2}}{144} + \frac{19 x}{6}

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