An expression describes a calculation without saying it equals a particular value. Letters stand for numbers, so the usual number rules still apply. Like terms have exactly the same letter part: 3x and 5x can combine, but 3x and 5 cannot. Expanding distributes multiplication to every term inside a bracket. Factorising reverses this by finding a factor shared by all terms. At the stretch end of Foundation, two brackets can be expanded by multiplying every term in one bracket by every term in the other, then collecting like terms.
Learning objectives
- Collect like terms and expand brackets.
- Factorise by taking out a common factor.
Key ideas
Like terms have exactly the same letter part, including powers.
Multiply the outside factor by every term in the bracket.
For two brackets, multiply every term in one by every term in the other.
Factorising reverses expansion. Take out the greatest common factor and check by expanding.
Use brackets when substituting a negative number into a power.
Worked examples
Example 1
Expand the bracket and collect like terms.
Answer
Example 2
Factorise fully using the greatest common factor.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Collect like terms, expand brackets, factorise or substitute a value.
AO2 · Reasoning
Decide whether two expressions are equivalent, using algebra rather than one example.
AO3 · Problem solving
Write an expression for a perimeter or cost and simplify it.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
Keep the negative sign when expanding. Unlike terms cannot be combined into a single term.
Try it yourself
Attempt each question before opening its answer.
Check 1: Factorise 12x + 18 fully.
Answer: 6(2x + 3)
The greatest common factor is 6. Dividing the two terms by 6 leaves 2x and 3.
Check 2: Expand (x + 2)(x + 3).
Answer: x² + 5x + 6
The four products are x², 3x, 2x and 6. Combine 3x + 2x to make 5x.
Explain it in your own words
- Write two like terms and two terms that are not alike.
- Use a rectangle model to explain 4(x + 3).
- Factorise your own two-term expression and expand to check it.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Algebra specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.