# Combining Like Terms Lots of times you’re going to have to do this crazy thing called “combining like terms.” I know it might seem like some arbitrary procedure invented by mathematicians to make you want to pull you hair out, but it’s actually super easy.

Remember our old friend the distributive law?  For all numbers a, b, and c, the following is true: a(b+c)=ab+ac? Of course you do. Combining like terms is just the application of the distributive law.  say we’ve got this problem, and the instructions are to “simplify”.

2x2+3x2

We use the distributive law, with x2 playing the role of “a”, 2 playing the role of “b” and 3 playing the role of “c”.

2x2+3x2=(2+3)x2

And you know what 2+3 is, right? Right.

2x2+3x2=(2+3)x2=5x2

How many x squareds do we have? 5! Easy peasy.

If you have a problem that’s a little more complicated, the same method applies.

2x2+3x+4x2+5x

First we rearrange terms using the commutative law of addition, so all the x squareds are with the x squareds and all the x’s are with all the x’s:

2x2+3x+4x2+5x
=2x2+4x2+3x+5x

Now do the same distributive law magic we did before:

2x2+3x+4x2+5x
=2x2+4x2+3x+5x
=(2+4)x2+(3+5)x