展开 ((x+5)/2)^2

解答

展开

(\frac{x + 5}{2})^{2}

\frac{x ^{2}}{4} + \frac{5 x}{2} + \frac{25}{4}

求解步骤

(\frac{x + 5}{2})^{2}

使用指数法则:

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

= \frac{( x + 5 ) ^{2}}{2 ^{2}}

(x + 5)^{2} = x^{2} + 10 x + 25

= \frac{x ^{2} + 10 x + 25}{2 ^{2}}

2^{2} = 4

= \frac{x ^{2} + 10 x + 25}{4}

使用分式法则:

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

\frac{x ^{2} + 10 x + 25}{4} = \frac{x ^{2}}{4} + \frac{10 x}{4} + \frac{25}{4}

= \frac{x ^{2}}{4} + \frac{10 x}{4} + \frac{25}{4}

消掉

\frac{10 x}{4} : \frac{5 x}{2}

= \frac{x ^{2}}{4} + \frac{5 x}{2} + \frac{25}{4}

e x p an d (e^{s t} + e^{- s t}) \cdot (e^{s x t} + e^{- s x t})

e x p an d (e^{j t} + e^{- j t})^{3}

e x p an d \frac{( 3 r + 1 ) ^{3}}{14 4 r + 1}

e x p an d 15 (1 - e^{- 0.04 t})

\frac{d}{d t} ((θ) (2 e^{2 t} - 4 e^{3 t}))