展开 (((n^2+3n+2)(2n+3)))/6

解答

展开

\frac{( ( n ^{2} + 3 n + 2 ) ( 2 n + 3 ) )}{6}

\frac{n ^{3}}{3} + \frac{3 n ^{2}}{2} + \frac{13 n}{6} + 1

求解步骤

\frac{( n ^{2} + 3 n + 2 ) ( 2 n + 3 )}{6}

乘开

(n^{2} + 3 n + 2) (2 n + 3) : 2 n^{3} + 9 n^{2} + 13 n + 6

= \frac{2 n ^{3} + 9 n ^{2} + 13 n + 6}{6}

使用分式法则:

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

\frac{2 n ^{3} + 9 n ^{2} + 13 n + 6}{6} = \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + \frac{6}{6}

= \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + \frac{6}{6}

使用法则

\frac{a}{a} = 1

\frac{6}{6} = 1

= \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + 1

消掉

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

= \frac{n ^{3}}{3} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + 1

消掉

\frac{9 n ^{2}}{6} : \frac{3 n ^{2}}{2}

= \frac{n ^{3}}{3} + \frac{3 n ^{2}}{2} + \frac{13 n}{6} + 1

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