Algebraic Expressions • Topic 5 of 7

Like and Unlike Terms

Like terms have exactly the same variable part — the same letters raised to the same powers — and differ only in their coefficients. So 3x and 7x are like terms, and 5x² and 2x² are like terms, but 3x and 3x² are not, because the powers differ. Only like terms can be combined, by adding or subtracting their coefficients; unlike terms stay separate. Constants are like terms with each other. Spotting like terms quickly is what makes simplifying expressions fast and accurate, and it is the foundation for solving equations.

✅ Solved examples

1. Are 4x and 9x like terms?
They have the same variable x to the same power, so yes — they are like terms.
2. Are 2x² and 5x like terms?
No; the powers differ (x² versus x), so they are unlike.
3. Combine 6y + 3y.
Like terms: add coefficients, 6 + 3 = 9, giving 9y.
4. Can 7 and 4 be combined?
Both are constants (like terms), so 7 + 4 = 11.

✏️ Practice — try these, take hints as needed

1. Are 5a and 8a like terms?
Same variable, same power?
Both are a to the first power.
Yes/no.
Yes.
2. Are 3x² and 3x like terms?
Compare the powers.
x² vs x differ.
Yes/no.
No.
3. Combine 10m − 4m.
Like terms: subtract coefficients.
10 − 4.
Keep m.
6m.
4. Combine 2x + 5x − 3x.
Add and subtract the coefficients.
2 + 5 − 3.
Keep x.
4x.
5. Can 3xy and 5xy be combined?
Same variable part xy?
Yes, same letters and powers.
Add coefficients.
Yes → 8xy.

📝 Topic test — 8 questions

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