展开 ((x^2-1)^3)/4

解答

展开

\frac{( x ^{2} - 1 ) ^{3}}{4}

\frac{x ^{6}}{4} - \frac{3 x ^{4}}{4} + \frac{3 x ^{2}}{4} - \frac{1}{4}

求解步骤

\frac{( x ^{2} - 1 ) ^{3}}{4}

(x^{2} - 1)^{3} = x^{6} - 3 x^{4} + 3 x^{2} - 1

= \frac{x ^{6} - 3 x ^{4} + 3 x ^{2} - 1}{4}

使用分式法则:

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

\frac{x ^{6} - 3 x ^{4} + 3 x ^{2} - 1}{4} = \frac{x ^{6}}{4} - \frac{3 x ^{4}}{4} + \frac{3 x ^{2}}{4} - \frac{1}{4}

= \frac{x ^{6}}{4} - \frac{3 x ^{4}}{4} + \frac{3 x ^{2}}{4} - \frac{1}{4}

e x p an d \frac{- 15 s + 4}{( s ^{2} - 13 s + 26 ) s}

e x p an d (2 x + y = 9,) (2 x - y = 11)

e x p an d (x^{4} + 4 x^{3} + 8 x^{2}) \cdot (x - 3 + 5)

e x p an d lo g_{2} (4 a c)

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