展开 (n(n-1)(n-2))/6

解答

展开

\frac{n ( n - 1 ) ( n - 2 )}{6}

\frac{n ^{3}}{6} - \frac{n ^{2}}{2} + \frac{n}{3}

求解步骤

\frac{n ( n - 1 ) ( n - 2 )}{6}

乘开

n (n - 1) (n - 2) : n^{3} - 3 n^{2} + 2 n

= \frac{n ^{3} - 3 n ^{2} + 2 n}{6}

使用分式法则:

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

\frac{n ^{3} - 3 n ^{2} + 2 n}{6} = \frac{n ^{3}}{6} - \frac{3 n ^{2}}{6} + \frac{2 n}{6}

= \frac{n ^{3}}{6} - \frac{3 n ^{2}}{6} + \frac{2 n}{6}

消掉

\frac{3 n ^{2}}{6} : \frac{n ^{2}}{2}

= \frac{n ^{3}}{6} - \frac{n ^{2}}{2} + \frac{2 n}{6}

消掉

\frac{2 n}{6} : \frac{n}{3}

= \frac{n ^{3}}{6} - \frac{n ^{2}}{2} + \frac{n}{3}

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