I have several that look like this that I need to factor. I just need to a walk-through of this please! Where do I start?
9y^{2} - 4x^{2} - 4x - 1
First take a look at the x terms. You pretty much have to recognize $\displaystyle -4x^2 - 4x - 1 = -(2x + 1)^2$. I can't think of any way to know how to do this aside from experience. (I first noted that 9y^2 is a perfect square. Start these by looking for something like that.) So your problem becomes:
$\displaystyle 9y^2 - 4x^2 - 4x - 1 = 9y^2 - (2x + 1)^2$
Look at the RHS. It is the difference of two squares. What can you do with that?
-Dan