I'll answer your second question first:
Let's assume Make the changes:Why are we able to do this again?
Hey look! I can pull u common factor!
Restore u now:
As for your second question: 2 variables in an expression is a good hint that it needs factoring by grouping.
Now you got a bag of tricks. How do you know which one to use? Try everything. Some expressions can be factored on the go. Other expressions needs some more work. Try all the easy ways first, and if that fails, then try the less easier ways, and so on. Eventually, with practice, you'll get the hang of it.