展开 (sqrt(n+2)-sqrt(n))*sqrt(n+1)

解答

展开

(n + 2 - n) \cdot n + 1

n^{2} + 3 n + 2 - n^{2} + n

求解步骤

(n + 2 - n) n + 1

= n + 1 (n + 2 - n)

使用分配律:

a (b - c) = ab - a c

n + 1 (n + 2 - n) = n + 1 n + 2 - n + 1 n

= n + 1 n + 2 - n + 1 n

化简

n + 1 n + 2 - n + 1 n : n^{2} + 3 n + 2 - n^{2} + n

= n^{2} + 3 n + 2 - n^{2} + n

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

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

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

e x p an d (x + 2 π)^{4}

e x p an d - (\frac{8 x}{y} - \frac{w}{t})^{2}