How does 3x(4x+5)-5(4x+5) factor out to be (4x+5)(3x-5) ? This may be wrong, because I wrote this answer in my notes, but could some one please explain this to me? Also, do you have any tips on factoring? I understand the concept when I see an example(Usually), but I have a very hard time actually doing it.

Question

drwls · Answer

You have two different terms (3x and -5) that both multiply (4x + 5) . You can add these two terms together into (3x - 5)

You are using the "distributive" rule that
(x + y)z = xz + yz
but in this case you are using it "backwards".

x, y and z can be constants or algebraic terms