展开 (4x(x^2-28x-196)(7+x))/(147)

解答

展开

\frac{4 x ( x ^{2} - 28 x - 196 ) ( 7 + x )}{147}

\frac{4 x ^{4}}{147} - \frac{4 x ^{3}}{7} - \frac{32 x ^{2}}{3} - \frac{112 x}{3}

求解步骤

\frac{4 x ( x ^{2} - 28 x - 196 ) ( 7 + x )}{147}

乘开

4 x (x^{2} - 28 x - 196) (7 + x) : 4 x^{4} - 84 x^{3} - 1568 x^{2} - 5488 x

= \frac{4 x ^{4} - 84 x ^{3} - 1568 x ^{2} - 5488 x}{147}

使用分式法则:

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

\frac{4 x ^{4} - 84 x ^{3} - 1568 x ^{2} - 5488 x}{147} = \frac{4 x ^{4}}{147} - \frac{84 x ^{3}}{147} - \frac{1568 x ^{2}}{147} - \frac{5488 x}{147}

= \frac{4 x ^{4}}{147} - \frac{84 x ^{3}}{147} - \frac{1568 x ^{2}}{147} - \frac{5488 x}{147}

消掉

\frac{84 x ^{3}}{147} : \frac{4 x ^{3}}{7}

= \frac{4 x ^{4}}{147} - \frac{4 x ^{3}}{7} - \frac{1568 x ^{2}}{147} - \frac{5488 x}{147}

消掉

\frac{1568 x ^{2}}{147} : \frac{32 x ^{2}}{3}

= \frac{4 x ^{4}}{147} - \frac{4 x ^{3}}{7} - \frac{32 x ^{2}}{3} - \frac{5488 x}{147}

消掉

\frac{5488 x}{147} : \frac{112 x}{3}

= \frac{4 x ^{4}}{147} - \frac{4 x ^{3}}{7} - \frac{32 x ^{2}}{3} - \frac{112 x}{3}

e x p an d (1 - cos (x) - sin (x))^{2}

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

e x p an d \frac{x - 4}{2 ( x + 4 )}

e x p an d \frac{e ^{- 2 s}}{s ( s ^{2} + 2 s + 4 )}

s im pl i f y (3 x^{3} - x)^{2}