Algebra Question(Part of a Larger Problem)

[undrcvrbro]

1. The problem statement, all variables and given/known data
f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2)

Need to simplify.


2. Relevant equations



3. The attempt at a solution
I tried simplifying completely but my answer wasn't even close. The Back of the book has:
5x(x-5)^(2)(x-2)

I know its easy, but I'm drawing a blank...can anyone start me off on the right path to find how they got that answer?

[Dick]

The first thing to notice is that both terms in your expression have a common factor of x*(x-5)^2. Factor that out. Now what's left in each term?

[undrcvrbro]

Well, wouldn't it then be 2(x-5) + (3x+1)?

[Dick]

I get just 2(x-5)+3x. Where did the 1 come from?

[undrcvrbro]

Oh wow. I can't believe I had made a mistake like that. Thank you so much. I just figured it out.

Thanks Dick.