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What Are Like Terms, and How Do You Combine Them?

what are like terms: boy writing

What are like terms? They are terms whose variables and exponents have the same value. If two terms have different variables or different exponents, they are called unlike terms. Here are some examples of like and unlike terms:

Like terms:

what are like terms: like terms

Unlike terms:

what are like terms: unlike terms

Let's break down the defining features of like terms and show you how to combine them.

What Are Like Terms?

The variable parts of like terms, such as variable x or y, must always be the same:

what are like terms: like terms with variables

The numerical coefficients, aka the number in front of the variable, do not have to match.

Not all like terms have to have exponents, but if they do, the exponents must match:

what are like terms: like terms with same exponents

Even though the following terms have the same variable, they are unlike terms because the value of their exponents are not the same:

unlike terms with different exponents

How to Combine Like Terms

Take a look at the following expression:

combination of like terms

As you can see, this algebraic expression is made of like and unlike terms. To simplify it, we’ll combine the like terms.

Let's walk through the process of simplifying expressions by identifying the like terms in the expression. To do this, we’ll look at the variables and exponents. We’ll keep the positive and negative signs of each value:

identifying like terms

We've taken the original expression and separated it into like terms. Since the value of 14 has no variables, it's considered a constant term.

Let's combine the rest of the like terms and simplify the expression:

combined like terms

Now that we've combined these like terms, let's write out our simplified expression:

simplified expression

Defining and Combining Like Terms — It's Easy!

Algebraic expressions with a lot of terms, variables, and exponents can be intimidating. But they become much less scary when you know how to identify and combine like terms.

Like terms have variables and exponents that match. When you know how to group the like terms of an expression, you can simplify and shorten them, making it much easier to solve.

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