What is expand (sqrt(n+2)-sqrt(n))*sqrt(n+1) ?

The solution to expand (sqrt(n+2)-sqrt(n))*sqrt(n+1) is sqrt(n^2+3n+2)-sqrt(n^2+n)

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expand (sqrt(n+2)-sqrt(n))*sqrt(n+1)

expand

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

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

Solution steps

(n + 2 - n) n + 1

= n + 1 (n + 2 - n)

Apply the distributive law:

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

Simplify

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

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

d x (x^{2} (1 - x)^{3})

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

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

2 (2 x^{2} + y^{2}) d x - x y d y

(x + 2 π)^{4}

What is expand (sqrt(n+2)-sqrt(n))*sqrt(n+1) ?
The solution to expand (sqrt(n+2)-sqrt(n))*sqrt(n+1) is sqrt(n^2+3n+2)-sqrt(n^2+n)