展开 (x(18-x)(36-x))/6

解答

展开

\frac{x ( 18 - x ) ( 36 - x )}{6}

\frac{x ^{3}}{6} - 9 x^{2} + 108 x

求解步骤

\frac{x ( 18 - x ) ( 36 - x )}{6}

乘开

x (18 - x) (36 - x) : 648 x - 54 x^{2} + x^{3}

= \frac{648 x - 54 x ^{2} + x ^{3}}{6}

使用分式法则:

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

\frac{648 x - 54 x ^{2} + x ^{3}}{6} = \frac{648 x}{6} - \frac{54 x ^{2}}{6} + \frac{x ^{3}}{6}

= \frac{648 x}{6} - \frac{54 x ^{2}}{6} + \frac{x ^{3}}{6}

数字相除:

\frac{648}{6} = 108

= 108 x - \frac{54 x ^{2}}{6} + \frac{x ^{3}}{6}

数字相除:

\frac{54}{6} = 9

= 108 x - 9 x^{2} + \frac{x ^{3}}{6}

改写为标准形式

= \frac{x ^{3}}{6} - 9 x^{2} + 108 x

e x p an d - 30 t + 780 (1 - e^{- \frac{t}{3}})

e x p an d (sin (x) - cos (x))^{2}

e x p an d \frac{1}{π ( a ^{2} - b ^{2} )} + \frac{4 b \cdot c}{π ( a ^{4} - b ^{4} )}

e x p an d \frac{( 2 - x ) ^{3}}{6}

e x p an d a (- 5, 2) b (4, - 3)