What Are Like Terms? Collecting Terms in KS3 Algebra

Like terms are terms in an algebraic expression that share exactly the same variable(s) raised to the same power. You can add or subtract like terms to simplify an expression — unlike terms cannot be combined.

What Makes Two Terms "Like"?

Two terms are like terms if they have identical variable parts. The coefficients (the numbers in front) can differ — only the variable part matters.

Term | Variable part | Like term for?
3x | x | 7x, −2x
5x² | x² | x², 4x²
4xy | xy | −xy, 2xy
6y | y | y, −3y

Notice: 3x and 3x² are not like terms because the powers differ.

How to Collect Like Terms (Step by Step)

Collecting like terms means grouping identical variable parts and summing their coefficients.

Example: Simplify 4x + 3y − x + 2y

Identify the x terms: 4x and −x

Combine: 4x + (−x) = 3x

Identify the y terms: 3y and 2y

Combine: 3y + 2y = 5y

Result: 3x + 5y

A common mistake is adding the variable letters together — you cannot turn 3x + 5y into 8xy.

Worked Examples

Example 1: 5a + 2b − 3a + b

a terms: 5a − 3a = 2a

b terms: 2b + b = 3b

Answer: 2a + 3b

Example 2: x² + 3x − 2x² + 7x − 1

x² terms: x² − 2x² = −x²

x terms: 3x + 7x = 10x

Constant: −1

Answer: −x² + 10x − 1

How Do You Spot Like Terms Quickly?

The fastest way to check whether two terms are alike is to cover up the coefficient (the number in front) and compare what is left. If the variable parts are character-for-character identical — same letters, same powers — they are like terms.

For example, 4ab and −7ba are like terms, because multiplication is commutative: ab and ba mean the same thing. Always rewrite products in alphabetical order (ba → ab) before comparing, so you do not miss a match.

Pair of terms | Like? | Reason
2x and 9x | Yes | Both have variable part x
3x² and 5x | No | Powers differ (x² vs x)
6mn and −mn | Yes | Both have variable part mn
4a and 4b | No | Different letters

Why Does Collecting Like Terms Matter for KS3 Algebra?

Collecting like terms is the foundation of algebraic simplification. You will use it when expanding brackets, solving equations, and factorising — so getting comfortable with it early pays dividends across your entire GCSE maths course. The DfE national curriculum for KS3 mathematics lists simplifying and manipulating algebraic expressions by collecting like terms as a core skill students should master in Year 7, before expanding brackets in Year 8.

Once you can confidently collect like terms, expressions that look intimidating become short and manageable. An expression like 3a + 2b − a + 5b − 4 reduces to just 2a + 7b − 4 in three quick steps. Examiners reward this clear, methodical working even when the final answer is wrong, so always show the grouping stage before writing your answer.

Common Mistakes to Avoid

Combining terms with different variables (3x + 4y ≠ 7xy)

Forgetting that a lone variable like x has a coefficient of 1 (x = 1x)

Changing the sign when subtracting (5x − 2x = 3x, not 7x)

Mixing up x² and x terms

Practice Questions

Try these before reading the answers:

Simplify 6m + 4n − 2m + n

Simplify 3p² + p − p² + 4p

Simplify 2x + 3y − x − y + 5

Answers: (1) 4m + 5n (2) 2p² + 5p (3) x + 2y + 5

Frequently Asked Questions

What are like terms in maths?

Like terms are algebraic terms that have identical variable parts (same letter or letters, same exponent). Only like terms can be added or subtracted; the coefficients change but the variable part stays the same.

Can you combine 3x and 3y?

No. 3x and 3y are not like terms — they have different variable letters. You can only combine terms that are identical in their variable part.

What happens if I add unlike terms by mistake?

You get an incorrect simplification. For example, 3x + 4y = 7xy is wrong — the expression cannot be simplified further because the terms are unlike. Leave them as 3x + 4y.

Is x the same as x¹?

Yes. Any variable with no visible exponent has an implied exponent of 1. So x = x¹, and both are like terms with 5x or −2x.