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Like Terms and Unlike Terms: 8 Simple Examples
📚 Part of the Algebra Clinic: every lesson on this topic, in one place.
Quick answer: like terms have exactly the same letters with the same powers, such as 3x and -5x, or 2a^2b and 7a^2b. Only like terms can be added or subtracted: 3x+5x=8x, but 3x+5y and 3x+2x^2 cannot be combined.
Understand like terms properly, and algebra will stop looking like a crowd of letters fighting on the page. Many Ghana SHS students struggle with algebra because they collect terms by appearance, not by meaning.
A learner sees 3x, 4y, 5x², and 2x, then starts adding anything that has a letter. That is where the trouble begins. In algebra, terms are not like terms just because they all contain letters. They are like terms because they have the same variable part.
This post will fix that gap with eight simple examples. We shall not rush. We shall diagnose the mistake, explain it clearly, and help the learner practice like a serious WASSCE Mathematics candidate.
📋 What the WAEC Chief Examiner reported
- On 2019 Question 2, “Candidates could not expand” (a + 9b)² “and hence could not factorize the given expression completely”.
- On 2021 Question 2, “Most of them did the substitution correctly but could not find the common denominator”.
- TMC note: the Core reports we checked (2011–2025) do not name “like terms” as a weakness on its own. It sits underneath the skills above.
How to win these marks back
- Group like terms by letter and power: 3x and −5x are like terms; x and x² are not.
- After expanding, collect like terms before you try to factorise.
- Rewrite the expression in one clean line before the next step.
Source: WAEC Chief Examiner’s Report, WASSCE 2019, Mathematics (Core); WAEC Chief Examiner’s Report, WASSCE 2021, Mathematics (Core).
Why many SHS students find like terms hard
Many students can repeat the phrase “collect like terms,” but they do not know what makes terms “like.” So they combine unlike terms and create answers that look short but are mathematically wrong.
For example, some learners write 3x + 4y = 7xy. Others write 2x + 5x² = 7x². These answers show a hidden gap: the learner is trying to simplify by force instead of checking whether the terms are truly alike.
Why students make mistakes in like terms
The mistake happens because learners focus only on the coefficient, or only on the letter, and forget the full variable part. In the term 5x^2, the coefficient is 5, but the variable part is x². In the term 5x, the variable part is x. These two are not the same.
Another cause is weak language. When we say “like,” learners may think it means “similar-looking.” But in algebra, like terms must have the same letters raised to the same powers.
What WAEC reports say about like terms
In WASSCE Mathematics, like terms appear in simplification, expansion, factorisation, equations, substitution, graphs, and word problems. A learner who cannot collect like terms properly will struggle across many topics, not only in basic algebra.
The curriculum expects learners to use symbols meaningfully. So the learner must know that x, x^2, xy, and y are different algebraic objects, even if they all contain letters.
How to Understand Like Terms Properly
Like terms are terms with the same variable part. The numbers in front may be different, but the letters and their powers must match.
| Terms | Are they like terms? | Reason |
| 3x and 7x | Yes | Both have x. |
| 4a and -9a | Yes | Both have a. |
| 2x and 2x^2 | No | x is not the same as x^2. |
| 5xy and 8xy | Yes | Both have xy. |
| 6x and 6y | No | x and y are different variables. |
8 Simple Examples to Understand Like Terms Properly
1. 3x + 5x = 8x. The terms are alike because both contain x.
2. 9a – 4a = 5a. Keep the letter a and subtract the coefficients.
3. 7y + 2x cannot be simplified. Y and X are different.
4. 5x^2 + 3x^2 = 8x^2. Both variable parts are x^2.
5. 6x^2 + 2x cannot be combined. x² and x are not the same.
6. 4ab + 9ab = 13ab. Both terms contain ab.
7. 8m – 3n + 2m = 10m – 3n. Collect only the m terms.
8. 2p + 5 – p + 7 = p + 12. The like terms are 2p and -p, and then 5 and 7.
Worked Example: Collecting Like Terms Step by Step
Simplify: 4x + 7y – 2x + 3y – 5
Step 1: Group the like terms with their signs.
4x – 2x + 7y + 3y – 5
Step 2: Combine the coefficients.
2x + 10y – 5
Final answer: 2x + 10y – 5
Common mistakes in like terms
\text{Wrong}: 4x + 7y - 2x + 3y - 5 = 12xy - 5
This is wrong because the learner joined x terms and y terms together as if all letters were the same. Algebra does not work like that. x terms stay with x terms. y terms stay with y terms. Constant numbers stay with constant numbers.
Correct Method Learners Should Use
- First identify the variable part of each term.
- Carry the sign with the term.
- Group terms that have the same letters and powers.
- Add or subtract only the coefficients.
- Leave unlike terms as they are.
Mini Clinic Box: To Understand Like Terms Properly, Change the Coefficients but Keep the Variable Parts the Same
When collecting like terms, the coefficient may change, but the variable part stays the same. That is why 3x + 5x becomes 8x, not 8x^2. We are counting x’s. We are not multiplying x by x.
Practice Task
Simplify the following:
1. 6x + 4x
2. 9a – 2b + 3a
3. 5x^2 + 2x^2 – x
4. 7m – 3 + 2m + 8
5. 4pq + 6p + 3pq
Answers:
1) 10x
2) 12a – 2b
3) 7x^2 – x
4) 9m + 5
5) 7pq + 6p
Conclusion: Like Terms Are Not a Guessing Game
To understand like terms properly, the learner must stop asking, “Do they all have letters?” and start asking, “Do they have the same variable part?” That small question fixes many algebra mistakes.
Once learners can identify like terms, they can simplify expressions, solve equations, expand brackets, and factorise with more confidence. Algebra becomes cleaner because every term knows where it belongs.
Keep learning
- Afraid of Algebra? 8 Beginner-Friendly Examples That Help
- Sign Errors in Mathematics: 9 Ways to Avoid Them
- 9 Ways to Stop Mixing Up Expressions and Equations
📚 See every lesson in the Algebra Clinic
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Written by
Dickson Sarpong
NTC-certified SHS Mathematics teacher in Ghana with WAEC marking experience, and author of The Bridge Series textbooks. Every lesson here is built around the mistakes WAEC examiners keep reporting.
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