展开 (2x-2+c/(e^x))^2

解答

展开

(2 x - 2 + \frac{c}{e ^{x}})^{2}

4 x^{2} - 8 x + \frac{4 c x}{e ^{x}} - \frac{4 c}{e ^{x}} + \frac{c ^{2}}{e ^{2 x}} + 4

求解步骤

(2 x - 2 + \frac{c}{e ^{x}})^{2}

(2 x - 2 + \frac{c}{e ^{x}})^{2} = (2 x - 2 + \frac{c}{e ^{x}}) (2 x - 2 + \frac{c}{e ^{x}})

= (2 x + \frac{c}{e ^{x}} - 2) (2 x + \frac{c}{e ^{x}} - 2)

乘开

(2 x - 2 + \frac{c}{e ^{x}}) (2 x - 2 + \frac{c}{e ^{x}}) : 4 x^{2} - 8 x + \frac{4 c x - 4 c}{e ^{x}} + \frac{c ^{2}}{e ^{2 x}} + 4

= 4 x^{2} - 8 x + \frac{4 c x - 4 c}{e ^{x}} + \frac{c ^{2}}{e ^{2 x}} + 4

使用分式法则:

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

\frac{4 c x - 4 c}{e ^{x}} = \frac{4 c x}{e ^{x}} - \frac{4 c}{e ^{x}}

= 4 x^{2} - 8 x + \frac{4 c x}{e ^{x}} - \frac{4 c}{e ^{x}} + \frac{c ^{2}}{e ^{2 x}} + 4

e x p an d \frac{4 x ^{2} + 3 x + 6}{x ^{2} ( x ^{2} + 3 )}

e x p an d x (51 - 8 ln (x))

e x p an d \frac{( tan ^{2} ( x ) )}{2} + \frac{( tan ^{4} ( x ) )}{4}

e x p an d \frac{( x y + 6 ) ^{3}}{8 y ^{3}}

e x p an d \frac{( ( x + 2 ) ( 2 a + x ) )}{2}