展开 ((x-3)(x-5)(x-7))/(48)

解答

展开

\frac{( x - 3 ) \cdot ( x - 5 ) \cdot ( x - 7 )}{48}

\frac{x ^{3}}{48} - \frac{5 x ^{2}}{16} + \frac{71 x}{48} - \frac{35}{16}

求解步骤

\frac{( x - 3 ) ( x - 5 ) ( x - 7 )}{48}

乘开

(x - 3) (x - 5) (x - 7) : x^{3} - 15 x^{2} + 71 x - 105

= \frac{x ^{3} - 15 x ^{2} + 71 x - 105}{48}

使用分式法则:

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

\frac{x ^{3} - 15 x ^{2} + 71 x - 105}{48} = \frac{x ^{3}}{48} - \frac{15 x ^{2}}{48} + \frac{71 x}{48} - \frac{105}{48}

= \frac{x ^{3}}{48} - \frac{15 x ^{2}}{48} + \frac{71 x}{48} - \frac{105}{48}

消掉

\frac{15 x ^{2}}{48} : \frac{5 x ^{2}}{16}

= \frac{x ^{3}}{48} - \frac{5 x ^{2}}{16} + \frac{71 x}{48} - \frac{105}{48}

消掉

\frac{105}{48} : \frac{35}{16}

= \frac{x ^{3}}{48} - \frac{5 x ^{2}}{16} + \frac{71 x}{48} - \frac{35}{16}

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