Factor the expression. ab - 2b^2 + ay - 2by

The factored form of this expression is (b + y)(a - 2b)

In order to find this, we need to use a method called factoring by splitting. in this method, we start by taking the first two terms and separating them. Then we take out the greatest common factor.

ab - 2b^2 > Greatest common factor is b

b(a - 2b)

Now we do the same with the second pair.

ay - 2by > Greatest common factor is y

y(a - 2b)

Since both leave behind the same parenthesis after pulling out the factors, we can express that parenthesis as being multiplied by the factors we pulled out. So, we use one parenthesis for the factors and the other for what was left behind in both problems.

(b + y)(a - 2b)