展开 ((-1+x)^5)/5

解答

展开

\frac{( - 1 + x ) ^{5}}{5}

\frac{x ^{5}}{5} - x^{4} + 2 x^{3} - 2 x^{2} + x - \frac{1}{5}

求解步骤

\frac{( - 1 + x ) ^{5}}{5}

(- 1 + x)^{5} = - 1 + 5 x - 10 x^{2} + 10 x^{3} - 5 x^{4} + x^{5}

= \frac{( - 1 + 5 x - 10 x ^{2} + 10 x ^{3} - 5 x ^{4} + x ^{5} )}{5}

去除括号:

(- a) = - a

= \frac{- 1 + 5 x - 10 x ^{2} + 10 x ^{3} - 5 x ^{4} + x ^{5}}{5}

使用分式法则:

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

\frac{- 1 + 5 x - 10 x ^{2} + 10 x ^{3} - 5 x ^{4} + x ^{5}}{5} = - \frac{1}{5} + \frac{5 x}{5} - \frac{10 x ^{2}}{5} + \frac{10 x ^{3}}{5} - \frac{5 x ^{4}}{5} + \frac{x ^{5}}{5}

= - \frac{1}{5} + \frac{5 x}{5} - \frac{10 x ^{2}}{5} + \frac{10 x ^{3}}{5} - \frac{5 x ^{4}}{5} + \frac{x ^{5}}{5}

\frac{5 x}{5} = x

\frac{10 x ^{2}}{5} = 2 x^{2}

\frac{10 x ^{3}}{5} = 2 x^{3}

\frac{5 x ^{4}}{5} = x^{4}

= - \frac{1}{5} + x - 2 x^{2} + 2 x^{3} - x^{4} + \frac{x ^{5}}{5}

改写为标准形式

= \frac{x ^{5}}{5} - x^{4} + 2 x^{3} - 2 x^{2} + x - \frac{1}{5}

e x p an d \frac{( 12 - 3 x ) ^{2}}{4}

e x p an d 9 x - 3 x + 5 (1 + 2 x = 7 x + 3 (x - 4))

e x p an d 2 ((5 y + 9) (2 y - 2))

e x p an d \frac{1}{lo g _{10} ( x ) ( 8 + x )}

s im pl i f y t^{2} H (t - 4) d t