展开 ((x-1)^4)/4

解答

展开

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

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

求解步骤

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

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

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

使用分式法则:

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

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

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

数字相除:

\frac{4}{4} = 1

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

消掉

\frac{6 x ^{2}}{4} : \frac{3 x ^{2}}{2}

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

数字相除:

\frac{4}{4} = 1

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

e x p an d (t + a)^{2} + e^{- a t} - 2 cos (a t)

e x p an d \frac{1 + 2 ^{n}}{3 ^{n - 1}}

e x p an d \frac{3 x ^{2} - 10 x - 5}{( x - 1 ) ^{2} ( x + 2 )}

e x p an d (5 - 2) (4 + 3)

e x p an d (t - 1) cosh (2 t)