展开 ((h+1)(h+2)(2h+3))/6

解答

展开

\frac{( h + 1 ) ( h + 2 ) ( 2 h + 3 )}{6}

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

求解步骤

\frac{( h + 1 ) ( h + 2 ) ( 2 h + 3 )}{6}

乘开

(h + 1) (h + 2) (2 h + 3) : 2 h^{3} + 9 h^{2} + 13 h + 6

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

使用分式法则:

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

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

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

使用法则

\frac{a}{a} = 1

\frac{6}{6} = 1

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

消掉

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

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

消掉

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

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

e x p an d U (t - π)

e x p an d z (a (z^{2} - a^{2}))

e x p an d \frac{( x - 3 )}{x ^{2} ( x - 5 )}

e x p an d \frac{x ^{3} + x ^{2} + 1}{x ( x - 1 ) ( x ^{2} + x + 1 ) ( x ^{2} + 1 )}

e x p an d y^{'} (x) (x)^{2} - (3 y^{2} + cos (x) y^{'} (x) + 3 y^{2} cos (x) = 0)