展开 |(((x+1)^3)/(2^x))-2|

解答

展开

(\frac{( x + 1 ) ^{3}}{2 ^{x}}) - 2

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

求解步骤

(\frac{( x + 1 ) ^{3}}{2 ^{x}}) - 2

去除括号:

(a) = a

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

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

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

使用分式法则:

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

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

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

e x p an d (x + 2 \cdot lo g_{2} (x)) (x - 2)

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

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

e x p an d (2 u, 2 v, 1) \cdot (9 - u^{2} - v^{2}, 9 - u^{2} - v^{2}, u)

e x p an d \frac{n ^{2}}{( - 2 i d x + 2 i ^{2} d ^{2} ) ( s + x - i d )}