展开 (125(2n+1)(n+1))/6

解答

展开

\frac{125 ( 2 n + 1 ) ( n + 1 )}{6}

\frac{125 n ^{2}}{3} + \frac{125 n}{2} + \frac{125}{6}

求解步骤

\frac{125 ( 2 n + 1 ) ( n + 1 )}{6}

乘开

125 (2 n + 1) (n + 1) : 250 n^{2} + 375 n + 125

= \frac{250 n ^{2} + 375 n + 125}{6}

使用分式法则:

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

\frac{250 n ^{2} + 375 n + 125}{6} = \frac{250 n ^{2}}{6} + \frac{375 n}{6} + \frac{125}{6}

= \frac{250 n ^{2}}{6} + \frac{375 n}{6} + \frac{125}{6}

消掉

\frac{250 n ^{2}}{6} : \frac{125 n ^{2}}{3}

= \frac{125 n ^{2}}{3} + \frac{375 n}{6} + \frac{125}{6}

消掉

\frac{375 n}{6} : \frac{125 n}{2}

= \frac{125 n ^{2}}{3} + \frac{125 n}{2} + \frac{125}{6}

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