can anybody explain how to factor this?

Question

i need an explaination on how to factor this

(x+1)^3/2 + x * 3/2(x+1)^1/2

i know the answer it's

1/2(5x+2)(x+1)^1/2

i just don't know how it got there

Answer 1

first term is (x+1)(√(x+1)), right
so both terms have √(x+1) so it factors out
leaving
(x+1) + 3x/2
rearranging
5x/2 + 1
so
(5x/2 +1)(√(x+1))

Answer 2

(x+1)^3/2 + x * 3/2(x+1)^1/2
Factor out the common factor (x+1)^1/2, getting:
(x+1)^1/2[(x+1)^1 + 3x/2]
= (x+1)^1/2(x+1+3x/2)
= (x+1)^1/2(5x/2+1)

Answer 3

=(x+1)^1/2{(x+1)+x*3/2}
=(x+1)^1/2{5/2x+1} ans