展开 ((x+1)/2)^2

解答

展开

(\frac{x + 1}{2})^{2}

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

求解步骤

(\frac{x + 1}{2})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( x + 1 ) ^{2}}{2 ^{2}}

(x + 1)^{2} = x^{2} + 2 x + 1

= \frac{x ^{2} + 2 x + 1}{2 ^{2}}

2^{2} = 4

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

使用分式法则:

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

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

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

消掉

\frac{2 x}{4} : \frac{x}{2}

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

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

s im pl i f y (x - i y + 1)^{2}

s im pl i f y - (x - 1) (x - 1 + 3) (x - 1 - 3)

e x p an d \frac{2 ( π - 2 2 )}{3 π - 8}

e x p an d \frac{5 ( - x ^{2} + 36 )}{( x ^{2} + 36 ) ^{2}}