Algebra Foundations

Combining Like Terms

Simplifying an expression by combining terms with the same variable.

Foundational15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Evaluating Expressions

Terms That Belong Together

You already know how to evaluate an expression once every variable has a number attached to it. But most of the time, you'll want to work with an expression before you know what the variables equal — and that means simplifying it first. Combining like terms is the most common way to make a messy expression shorter and easier to work with.

Definition — Like Terms

Terms that have the exact same variable raised to the exact same power. 3x and 5x are like terms because they both have x to the first power. 3x and 5x² are not like terms, even though they share the same variable, because the powers don't match.

A term is a single piece of an expression — a number, a variable, or a number and variable multiplied together, separated from the rest of the expression by a plus or minus sign. In the expression 4x + 7 − 2x, there are three terms: 4x, 7, and −2x.

To combine like terms, add or subtract their coefficients — the numbers multiplied by the variable — and keep the variable part exactly as it was. Think of it the way you'd count objects: 4 apples plus 2 apples is 6 apples, not 6 apples-squared or 6 oranges. The 'apples' stay the same; only the count changes.

Worked Example — Combining Two Like Terms

Simplify 4x + 7 − 2x. First, identify the like terms: 4x and −2x both have x to the first power, so they can combine. The 7 has no variable at all, so it stands alone. Combining 4x and −2x gives (4 − 2)x = 2x. The simplified expression is 2x + 7.

Worked Example — Combining Terms with More Than One Variable

Simplify 5a + 3b − a + 2b. There are two families of like terms here: the a-terms (5a and −a) and the b-terms (3b and 2b). Combine each family separately: 5a − a = 4a, and 3b + 2b = 5b. The simplified expression is 4a + 5b — it can't be combined any further because a and b are different variables.

Tip

If a term is just a variable by itself, like the −a in the example above, its coefficient is understood to be −1, even though the 1 isn't written. Rewriting −a as −1a before combining can help until this becomes automatic.

Common Mistakes

Combining 3x and 5x² into 8x or 8x², treating them as like terms.
Check the exponent on the variable, not just the letter. 3x and 5x² have different powers of x, so they are not like terms and cannot be combined.
Dropping the sign in front of a term when reordering an expression, such as rewriting 4x − 2x + 7 as 4x + 2x + 7.
The sign directly in front of a term belongs to that term. Keep each term attached to the sign that precedes it, even when you move terms around to group like terms together.

Key Takeaways

Like terms have the same variable raised to the same power.
To combine like terms, add or subtract their coefficients and keep the variable part unchanged.
An expression with different variables (like 4a + 5b) is already fully simplified once no more like terms remain.

Summary

Combining like terms turns a longer expression into an equivalent, shorter one by merging terms that share the same variable and exponent. This simplifying skill is exactly what you'll need next, when solving equations means isolating a variable on one side.

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