展开 ((x-1)(2x-1)(4x-1))/8

解答

展开

\frac{( x - 1 ) ( 2 x - 1 ) ( 4 x - 1 )}{8}

x^{3} - \frac{7 x ^{2}}{4} + \frac{7 x}{8} - \frac{1}{8}

求解步骤

\frac{( x - 1 ) ( 2 x - 1 ) ( 4 x - 1 )}{8}

乘开

(x - 1) (2 x - 1) (4 x - 1) : 8 x^{3} - 14 x^{2} + 7 x - 1

= \frac{8 x ^{3} - 14 x ^{2} + 7 x - 1}{8}

使用分式法则:

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

\frac{8 x ^{3} - 14 x ^{2} + 7 x - 1}{8} = \frac{8 x ^{3}}{8} - \frac{14 x ^{2}}{8} + \frac{7 x}{8} - \frac{1}{8}

= \frac{8 x ^{3}}{8} - \frac{14 x ^{2}}{8} + \frac{7 x}{8} - \frac{1}{8}

数字相除:

\frac{8}{8} = 1

= x^{3} - \frac{14 x ^{2}}{8} + \frac{7 x}{8} - \frac{1}{8}

消掉

\frac{14 x ^{2}}{8} : \frac{7 x ^{2}}{4}

= x^{3} - \frac{7 x ^{2}}{4} + \frac{7 x}{8} - \frac{1}{8}

e x p an d - \frac{s}{( s - a ) ( s ^{2} + 81 )}

e x p an d \frac{1}{( 2 + π ) ^{10}}

e x p an d 48 (\frac{5}{6} x + 2 = \frac{7}{8})

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

e x p an d (x cos^{2} (\frac{y}{x}) - y) d x + x d y