The purpose of combining like terms is to reduce the number of terms in an expression. Addition and subtraction are both forms of combining like terms. When you do an operation such as 3+4 -> 7, you are actually combining like terms! We’ll explain further:

What does it mean when you say “Like Terms”?
The first step in combining like terms is to understand what like terms are.

Here are the rules for determining like terms:

Rule 1: The terms must have all the same variables.
For example, 2x and 6x are like terms because they have the same variable (x). Now you might be thinking that 2x² and 6x are also like terms, which brings us to rule 2.

Rule 2: The exponent of the variables must be the same.
Since the x is squared (has an exponent of 2) in 2x² and the x in 6x is not, these are NOT like terms.

Ok, so what about 2x²y and 8x² ? They both contain x², but the 8x² does not contain a y variable - these are not like terms.

Here are some examples of like terms:

2x, 8x, -3x, -6x
-4y², 64y², 3y², -34634y²
2xyz,-9xyz, 10xyz

Here are some examples of unlike terms:

2x, 8y
x², x³
2xz,-9xy

How to combine like terms
Once we’ve identified at least two like terms in an expression we can begin to combine the like terms. Let’s look at an example:

3x+5y+2x-3y

First, we’ll identify the like terms:

3x and 2x are like terms, and so are 5y and -3y. Now that we have identified the like terms, we can combine them just as we would two constants. For the first set of like terms, we’ll combine the coefficients:

3x+2x

(3+2)x

5x

Now our new expression is…

5x+5y-3y

…but wait, we can combine the like y terms as well by combining the coefficients (in this case, subtracting).

5x + (5-3)y

5x+2y

And that’s it! We’ve combined all like terms in the expression 3x+5y+2x-3y to find the answer: 5x+2y.