展开 ((2x-1)^7)/(14)

解答

展开

\frac{( 2 x - 1 ) ^{7}}{14}

\frac{64 x ^{7}}{7} - 32 x^{6} + 48 x^{5} - 40 x^{4} + 20 x^{3} - 6 x^{2} + x - \frac{1}{14}

求解步骤

\frac{( 2 x - 1 ) ^{7}}{14}

(2 x - 1)^{7} = 128 x^{7} - 448 x^{6} + 672 x^{5} - 560 x^{4} + 280 x^{3} - 84 x^{2} + 14 x - 1

= \frac{128 x ^{7} - 448 x ^{6} + 672 x ^{5} - 560 x ^{4} + 280 x ^{3} - 84 x ^{2} + 14 x - 1}{14}

使用分式法则:

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

\frac{128 x ^{7} - 448 x ^{6} + 672 x ^{5} - 560 x ^{4} + 280 x ^{3} - 84 x ^{2} + 14 x - 1}{14} = \frac{128 x ^{7}}{14} - \frac{448 x ^{6}}{14} + \frac{672 x ^{5}}{14} - \frac{560 x ^{4}}{14} + \frac{280 x ^{3}}{14} - \frac{84 x ^{2}}{14} + \frac{14 x}{14} - \frac{1}{14}

= \frac{128 x ^{7}}{14} - \frac{448 x ^{6}}{14} + \frac{672 x ^{5}}{14} - \frac{560 x ^{4}}{14} + \frac{280 x ^{3}}{14} - \frac{84 x ^{2}}{14} + \frac{14 x}{14} - \frac{1}{14}

\frac{128 x ^{7}}{14} = \frac{64 x ^{7}}{7}

\frac{448 x ^{6}}{14} = 32 x^{6}

\frac{672 x ^{5}}{14} = 48 x^{5}

\frac{560 x ^{4}}{14} = 40 x^{4}

\frac{280 x ^{3}}{14} = 20 x^{3}

\frac{84 x ^{2}}{14} = 6 x^{2}

\frac{14 x}{14} = x

= \frac{64 x ^{7}}{7} - 32 x^{6} + 48 x^{5} - 40 x^{4} + 20 x^{3} - 6 x^{2} + x - \frac{1}{14}

e x p an d x^{2} - 4^{2}

e x p an d \frac{0.5 z}{( z - 0.5 ) ( z - 0.7 )}

e x p an d (x - \frac{π}{2}) \cdot (x - π)

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

\frac{\partial}{\partial x} ((f (x, y)) (x^{2} - x y))