Combining Like Terms — Rules, Examples, and Practice

By MathPal Editorial Team·Published Apr 17, 2026

Grade: 7-8 | Topic: Algebra

What You Will Learn

Combining like terms is one of the most fundamental skills in algebra. Every time you simplify an expression or solve an equation, you will use it. In this guide you will learn what makes terms "like," how to identify the coefficient and variable parts of a term, and how to combine terms correctly — even in multi-variable expressions with negative numbers.

Theory

What is a term?

A term is a single piece of an algebraic expression — a number, a variable, or a number multiplied by one or more variables. Terms are separated by $+$ or $-$ signs.

In the expression $4x + 7y - 3$, there are three terms: $4x$, $7y$, and $-3$.

Every term has two parts:

• Coefficient — the numerical factor in front of the variable. In $4x$, the coefficient is $4$. If no number is written, the coefficient is $1$ (so $x$ really means $1x$). A bare negative sign means $-1$ (so $-x$ means $-1x$).
• Variable part — the letter(s) and their exponents. In $4x$, the variable part is $x$.

A term with no variable at all, such as $-3$, is called a constant term.

What are like terms?

Like terms are terms whose variable parts are identical — the same variables raised to the same powers. Only the coefficients can differ.

Like terms	NOT like terms
$3x$ and $-5x$	$3x$ and $3x^{2}$
$2ab$ and $-ab$	$2ab$ and $2a$
$7$ and $-12$ (constants)	$4x$ and $4y$

How to combine like terms

To combine like terms, add or subtract their coefficients and keep the variable part unchanged:

$5x + 3x = (5 + 3)x = 8x$

$9y - 4y = (9 - 4)y = 5y$

When an expression has several different variable groups, combine each group separately:

$2x + 5y + 3x - y = (2x + 3x) + (5y - y) = 5x + 4y$

Working with negative coefficients

Negative signs belong to the term that follows them. Treat subtraction as adding a negative:

$7a - 10a = (7 + (-10))a = -3a$

$-2m - 5m = (-2 + (-5))m = -7m$

Worked Examples

Example 1 — Simple one-variable expression

Simplify $6x + 2x - x$.

Step 1: Identify like terms. All three terms contain $x$.

Step 2: Add the coefficients: $6 + 2 + (-1) = 7$.

Step 3: Write the result: $7x$.

Example 2 — Multi-variable expression

Simplify $3a + 4b - 2a + b$.

Step 1: Group the $a$-terms and $b$-terms:

$(3a - 2a) + (4b + b)$

Step 2: Combine each group:

$1a + 5b = a + 5b$

Example 3 — Expression with exponents

Simplify $5x^{2} + 3x - 2x^{2} + 7x + 4$.

Step 1: Identify the groups:

• $x^{2}$ terms: $5x^{2}$ and $-2x^{2}$
• $x$ terms: $3x$ and $7x$
• Constants: $4$

Step 2: Combine each:

$(5 - 2)x^{2} + (3 + 7)x + 4 = 3x^{2} + 10x + 4$

Example 4 — After the distributive property

Simplify $2(3x + 4) + 5x - 1$.

Step 1: Distribute: $6x + 8 + 5x - 1$.

Step 2: Group: $(6x + 5x) + (8 - 1)$.

Step 3: Combine: $11x + 7$.

Common Mistakes

Mistake 1 — Combining unlike terms

❌ $3x + 4x^{2} = 7x^{2}$

✅ $3x + 4x^{2}$ — these are NOT like terms (different exponents on $x$), so the expression is already simplified.

Mistake 2 — Forgetting the coefficient of 1

❌ $x + 5x = 5x$

✅ $x + 5x = 1x + 5x = 6x$ — remember that $x$ alone has a coefficient of $1$.

Mistake 3 — Dropping the negative sign

❌ $8y - 3y - 2y = 7y$

✅ $8y - 3y - 2y = (8 - 3 - 2)y = 3y$ — subtract both $3$ and $2$ from $8$.

Practice Problems

Problem 1: Simplify $4m + 9m$.

Show Answer

$4m + 9m = 13m$

Problem 2: Simplify $7x - 3x + 2$.

Show Answer

$7x - 3x + 2 = 4x + 2$

Problem 3: Simplify $2a + 3b - a + 5b$.

Show Answer

$(2a - a) + (3b + 5b) = a + 8b$

Problem 4: Simplify $6x^{2} - x + 4x^{2} + 3x - 5$.

Show Answer

$(6x^{2} + 4x^{2}) + (-x + 3x) + (-5) = 10x^{2} + 2x - 5$

Problem 5: Simplify $3(2y - 1) + 4y + 7$.

Show Answer

First distribute: $6y - 3 + 4y + 7$.

Then combine: $(6y + 4y) + (-3 + 7) = 10y + 4$.

Summary

• Like terms share exactly the same variable(s) raised to the same power(s).
• To combine like terms, add or subtract the coefficients and keep the variable part the same.
• Always watch for hidden coefficients of $1$ or $-1$.
• Group terms by their variable part before combining to stay organized.
• Combining like terms is used constantly in simplifying expressions, solving equations, and working with polynomials.

Related Topics

• Variables and Expressions — understand the building blocks of algebra
• Linear Equations — use combining like terms to solve equations
• Distributive Property — expand brackets before combining

---

Need help with combining like terms? Take a photo of your math problem and MathPal will solve it step by step. Open MathPal