Let's just dive right in!

What can you undistribute (no, that's not a real word) in this?

2x + 2y = 2 ( x + y ) ...the 2 can be factored out

If you don't believe me, distribute
2 back in to see if it works.

This is one of the main games of factoring -- undistributing things. We'll call it "taking out" or "factoring out."

What can we take out of this?

5x^2 + 10x = 5x ( x + 2 ) ...a 5x can be factored out

OK, now check this guy out -- and be careful! Always distribute to check it.

9x^2 - 3x = 3x ( 3x -1 ) ...the 3x can be factored out ...the -1 serves as a placeholder