---
title: "Collecting Like Terms"
description: "Simplify algebraic expressions by collecting like terms: combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence"
canonical: https://lightmysky.com/learn/mathematics/collecting-like-terms-mt_nNNVrLqPW3
source: https://lightmysky.com/learn/mathematics/collecting-like-terms-mt_nNNVrLqPW3.md
retrieved: 2026-10-19
---

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# Collecting Like Terms

Simplify algebraic expressions by collecting like terms: combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence

Subject: Mathematics · Area: Algebra · Ages 11 to 12
Page: https://lightmysky.com/learn/mathematics/collecting-like-terms-mt_nNNVrLqPW3

## Ready when they can

- Identify like terms in an algebraic expression
- Combine like terms involving positive and negative coefficients
- Simplify expressions involving multiple variables and constant terms

## Lesson: Collecting Like Terms

An expression can have several terms, like 3a + 2b + 5a. Some of these terms are like terms: they have the exact same variable raised to the same power. Only the coefficient, the number in front, can be different. 3a and 5a are like terms. 3a and 2b are not, because the letters are different.

*(drawing: Look at 3a + 2b + 5a. The terms 3a and 5a are like terms, so add their coefficients: 3 + 5 = 8. That gives 8a. The 2b has no partner, so it stays the same. The simplified expression is 8a + 2b.)*

**Example.** Negative coefficients work the same way: add the signed numbers in front. In 7m - 2m + 4, 7 + (-2) = 5, giving 5m + 4. The answer can land below zero: for 3n - 5n, start at 3 and count 5 back, 2, 1, 0, -1, -2, so you get -2n. Two minus terms join: -2t - 4t = -6t. And -3q + q = -2q, since one step up from -3 is -2.

Only combine terms that match exactly: same letter, same power. Never fold a constant into a term that has a letter, and never multiply the letters together when you collect terms.

**Recap.** Collecting like terms means adding or subtracting the coefficients of terms that share the same variable and power, and leaving everything else untouched.

## Practice

20 questions on this page, each with its working shown.

## Needs first

- [Expressions & Equations Vocabulary](https://lightmysky.com/learn/mathematics/expressions-and-equations-vocabulary-mt_g_fkAqmz72)

## Opens up

- [Expanding Single Brackets](https://lightmysky.com/learn/mathematics/expanding-single-brackets-mt_FX4a2Q8XXN)
- [Expanding Double Brackets](https://lightmysky.com/learn/mathematics/expanding-double-brackets-mt_KhS7K1Mgrw)