GCSE MATHS • FOUNDATION & HIGHER
Collecting Like Terms Made Simple
Learn how to identify like terms, combine coefficients and simplify algebraic expressions accurately using a clear step-by-step method.
Clear method
Exam practice
Worked proofs
Proof in Four Moves
1
Identify
Find terms containing exactly the same variables raised to the same powers.
2
Group
Place matching terms together, keeping the sign attached to each term.
3
Calculate
Add or subtract the numerical coefficients.
4
Rewrite
Write the simplified expression while keeping the variable part unchanged.
What You’ll Learn
Recognise Like Terms
Identify terms that contain the same variables raised to the same powers.
Separate Unlike Terms
Understand why terms with different variables or powers cannot be combined.
Combine Coefficients
Add or subtract the numbers placed before matching variables.
Handle Negative Terms
Keep negative signs attached to their terms when simplifying expressions.
Key Rules
Same Variable and Power
3x and 7x are like terms
Combine the Coefficients
3x + 5x = 8x
Different Powers Stay Separate
3x² + 5x cannot be simplified
Constants Combine Separately
4x + 8 + 6x + 3 = 10x + 11
Worked Proof: Consecutive Numbers
1. Identify
The like variable terms are 4x and 6x. The constants are 8 and 3.
2. Group
(4x + 6x) + (8 + 3)
3. Calculate
4x + 6x = 10x and 8 + 3 = 11
4. Write the Final Answer
10x + 11
More Worked Examples
1
Adding Like Terms
6x + 9x = 15x
2. Add the coefficients: 6 + 9 = 15.
2
Subtracting Like Terms
12a − 8a = 4a
2. Subtract the coefficients: 12 − 8 = 4.
3
Working with Negative Constants
9y − 4 + 2y − 7
2. Simplify each group.
4
Collecting Terms with Powers
8x² + 3x − 2x² + 5x
2. Simplify each group.
- Common GCSE Mistakes
- Combining unlike terms
- Changing the power
- Ignoring negative signs
- Combining different powers
- Forgetting constants
- Exam Tips
- Circle or underline terms containing the same variables and powers.
- Keep the positive or negative sign attached to each term.
- Group squared terms, linear terms and constants separately.
- Show the grouping step when an expression contains several types of terms.
- Check that no like terms remain in your final expression.
Ready to Practise?
Printable Worksheet
Practise identifying, grouping and simplifying like terms using printable questions with answers.
Interactive Quiz
Test your understanding of like and unlike terms with instant feedback.
Exam-Style Questions
Apply collecting like terms to longer GCSE algebra questions.
Watch the Collecting Like Terms Tutorial
Follow a clear step-by-step explanation of identifying like terms, combining coefficients, managing negative signs and simplifying expressions containing powers.
Frequently Asked Questions
Like terms contain exactly the same variables raised to the same powers. For example, 3x and 7x are like terms because they both contain x. However, 3x and 3y are unlike terms because their variables are different.
No. The terms contain the same variable but have different powers. They must remain separate. For example, 4x² + 3x is already simplified because x² and x are unlike terms.
Keep the negative sign attached to the coefficient. For example, 7a − 10a = 7a + (−10a) = −3a. Treating the sign as part of the term helps prevent subtraction errors.
No. Only the coefficients are added or subtracted. The variable and its power remain unchanged. For example, 3x² + 5x² = 8x². It does not become 8x⁴.
