展开 (((x+1)(x+2)(2x+3)))/6

解答

展开

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

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

求解步骤

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

乘开

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

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

使用分式法则:

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

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

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

使用法则

\frac{a}{a} = 1

\frac{6}{6} = 1

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

消掉

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

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

消掉

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

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

e x p an d \frac{6 x - 42}{( x - 4 ) ( x - 6 )}

e x p an d cos (π (0.5 + h))

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

e x p an d (12 x + 4 y = 15, 2) (32 x + 12 y = 420)

s im pl i f y 2 e^{- i (t + \frac{π}{4})}