In order to factor, we must pull out factors common to each term. In this case, each term has factors of 2 and y:
4ay = 2 * 2 * a * y
2y = 2 * y
So, we'll pull out the 2y:
[tex]2y(2a-1)[/tex]
To check, distribute the 2y back through the terms in parentheses to ensure you end up with the original expression 4ay - 2y.
