What Are Variable Terms?

Whenever you’re working with algebra, it’s really important that you know what a term is. The terms of an expression are separated by pluses and minuses:

$$12+3-6=9.$$

In this number sentence, 12 is a term, but so is $+3$ and $-6$. The number 9 is the sum of all the terms.

You’ll now see how things turn out when we invite variables to the party. The terms are separated in exactly the same way. Whenever you see a $+$ or $-$, a new term is formed. All terms start with either a plus sign or a minus sign. Remember: If you notice that there isn’t a sign written in front a term, you’re actually looking at an invisible $+$!

A numerical expression consists of terms. Adding one term to another is called a sum, while subtracting one term from another is called a difference.

When you add or subtract terms containing variables, you can only do so with terms that are like. Terms are like when they have the same combination of variables, and the same degree, or exponent. The numbers in front of the terms—the coefficients—don’t have to be the same.

$4a$ is an algebraic expression with a single term. If you connect more terms, both like and unalike, it might look like this:

$$4a+5b-3a$$

Here $4a$ is a term, $+5b$ is another term, and $-3a$ is the last term. As you can see, I’ve written the sign for each term. I do this to make sure I will always remember what term the sign belongs to. There’s also an invisible $+$ in front of $4a$.

So far you’ve only seen expressions with like variables. But what happens if the terms have unlike variables? The method you should use is called collection.

In the examples below you will see that each term is marked with a color. Terms that are like will have the same color.