I need someone to tell me if I'm right or wrong...

[magnum]

I've tried 3 different forums and none of them are helping.

The attached imaged is the problem I'm currently trying to solve. I'm not so great at factoring.

Direcitons: Simplify by factoring

My steps:
3(2x-1)^(1/2) (x+1)^2 - 2(2x-1)^(3/2) (x+1)
= (x+1)(2x-1)^(1/2) [3(x+1)-2(x-1)]
= (x+1)(2x-1)^(1/2) [3x+1-4x+2]
= (x+1)(2x-1)^(1/2) (3-x)

Did I factor it out correctly? If not, can someone list the steps and what I did wrong. Thanks in advance.

 

[Loren]

One mistake in your third line.

= (x+1)(2x-1)^(1/2) [3x+1-4x+2]

 

[Denis]

3(2x-1)^(1/2) (x+1)^2 - 2(2x-1)^(3/2) (x+1)
= 3(2x-1)^(1/2) (x+1)^2 - 2(2x-1)^(1/2) (2x-1) (x+1) : remember that a^(3/2) = a^(1/2) a^1
= (2x-1)^(1/2) (x+1) [3(x+1) - 2(2x-1)]

Easier if you go this way:
let a = 2x-1 and b = x+1

3a^(1/2) b^2 - 2a^(3/2) b
= 3a^(1/2) b^2 - 2a^(1/2) a b
= a^(1/2) b (3b - 2a)

Now substitute back in.