Having a very hard time in my PRECALC CLASS

[DeepSpace9]

Having a very hard time in my PRECALC CLASS.
When they facto problems they start pulling numbers out of numbers that aren't there..
Example..

3(4x+5)^2 (4)(5x+1)^2 + (4x+5)^3 (2) (5x+1)(5)

Professor said this was the answer.

a) 2(4x+5)^2(5x+1)[6(5x+1)+5(4x+5)]
=
b) 2(4x+5)^2(5x+1)[50x+31] (After combining like terms)

My questions is

Where I labeled a) where did she get the 6 from and the 5 from?
I can see she got the 5 from the original problem, but I thought if she factored out a 2 as a GCF the 5 would be reduced to a smaller number, and the 6 comes out of no where.. HELP

 

[DeepSpace9]

Thanks for the help guys.

 

[chiro]

Hey DeepSpace9.

Recall that 3*4 = 12 = 6*2 and 5*2 = 10 = 5*2 [Look at the factorization again carefully with the hint mentioned]

 

[DeepSpace9]

So the 6 comes from the fact that (3)(4) = 12 and since I factor out a (2) I would need a (6) to = 12 again? I didn't think we could use a 6 since it was not in the original problem.

 

[chiro]

Yes that's pretty much it.