How to Add and Subtract Variables

Here you’ll learn how to add and subtract variable expressions.

You can only add together like terms. If two or more terms have the same variable or combination of variables, then they are like, and you can add them. When you add two terms together, it looks like this:

$$3a+2a=5a$$

That’s because

$$3a+2a=\underbrace{a+a+a}\underbrace{+a+a}=5a.$$

As you can see, the only thing you need to do is add the numbers in front of the variables—the coefficients—together. This sum tells you how many you have of a given variable or combination of variables. In this case you have a total of five $a$’s.

Given what you’ve just learned, maybe you have an idea about how you subtract terms from each other! As you may have guessed, you can only subtract terms that are like, too. You do it in the same way you subtract numbers. When you subtract like terms, it looks like this:

$$3a-2a=1a=a$$

That’s because

$$\begin{array}{llll}\hfill 3a-2a& =\underbrace{a+a+a}\underbrace{-a-a}& \hfill & \\ \hfill & =\underset{0}{\underbrace{a-a}}\underset{0}{\underbrace{+a-a}}+a& \hfill & \\ \hfill & =1a& \hfill & \\ \hfill & =a.& \hfill & \end{array}$$

As you can see, it’s enough to subtract the coefficients in front of the variables. The difference tells you how many of a given variable you’re left with after subtracting.

When you need to add terms together, or subtract them from each other, this is what you do:

Here are some examples of how to add and subtract terms with variables. Put the terms in alphabetical order, with the terms including only numbers last.