Variables are like the Regan McNeil of algebra. Each variable used to be a cute little number but then they made the bad choice to play with a Ouija board wherein Captain Howdy turns them into pea soup spitting letters of fear and uncertainty. Yes, they seem scary, but basically are just a demon-possessed number masquerading as a letter.
With variables, your job is to figure out what number that letter used to be to free them of their demon. Yup, each math problem where you are solving for a variable is a mini exorcism!
The distributive property in algebra can be likened to the movie Rosemary's Baby. You take possessed numbers (aka variables) and their mates (should they have any) and spread their seed into the other numbers in the parentheses next door. Once everyone is done with their multiplying orgy of the damned, you combine like terms into teams, that is, demon numbers combine by addition or subtraction, as do plain ole numbers who have avoided being possessed. They are organized from most possessed to least possessed as follows:
* note- this concept works with possessing aliens also!
Factoring is the paternity test of algebra. Where did all these variables come from? How do I get rid of them!? How did I get to be such a great lawyer even though I talk like a surfer pretending to have a southern accent? Well, let's take a look at who the parents REALLY were.
In factoring with variables, you want to get it so that you end up with the parents; the groups of entities that created the original problem.
To do this you separate out as much of the variable expression as you can.
VARIABLE EXPRESSION!? Yes, variable expression...
15y would be an example of a variable expression. It means that there are 15 double possessed y's.
y+2 would also be an example of a variable expression.
Variable expressions would be the entities I was talking about above. In the case of horror movies, it is usually just a very religious woman and the devil. In the case below, it is and (1+4x).