GCSE & IGCSE maths practice

Expanding brackets questions and answers

Expanding brackets means multiplying everything inside a bracket by what's outside it, then collecting like terms. The questions start with single brackets, then double brackets and squared brackets, and finish with Higher-tier triple brackets and a short proof.

15 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 10 Nov 2026.

Start the questions Expanding brackets: the full guide Expanding brackets calculator

Where expanding brackets comes up

GCSE (AQA, Edexcel, OCR)	Single brackets and products of two binomials: Foundation and Higher. Products of three or more binomials: Higher only.
Cambridge IGCSE (0580)	Expanding products, e.g. (2x + 1)(x − 4): Core. Products of more than two brackets: Extended.
Edexcel International GCSE (4MA1)	Two simple linear brackets: Foundation. Two or more linear brackets, e.g. (x + 2)(x + 3)(x − 1): Higher.

The method

Single bracket: multiply every term inside by the term outside.
Double brackets: multiply each term in the first bracket by each term in the second (four products), then collect like terms.
A squared bracket means the bracket times itself: (x − 3)² = (x − 3)(x − 3).
Triple brackets (Higher): expand two of them first, then multiply the result by the third.

Expanding brackets questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Expand $5(x - 3)$

Question 2Warm-upFoundation

Expand $x(2x + 7)$

Question 3Warm-upFoundation

Expand $4(2a - 3b)$

Question 12Warm-upFoundation

Expand $-3(2x - 5)$

Exam-style

Question 4Exam-styleFoundation

Expand and simplify $3(x + 4) + 2(x - 5)$

Question 5Exam-styleFoundation

Expand and simplify $(x + 5)(x + 2)$

Question 6Exam-styleFoundation

Expand and simplify $(x - 6)(x + 4)$

Question 7Exam-styleFoundation

Expand and simplify $(x - 3)^2$

Question 8Exam-styleHigher

Expand and simplify $(2x + 3)(3x - 1)$

Question 9Exam-styleHigher

Expand and simplify $(x + 1)(x + 2)(x + 3)$

Question 13Exam-styleFoundation

Expand and simplify $(x + 7)(x - 7)$

Question 14Exam-styleHigher

Expand and simplify $(3x - 2)^2$

Challenge

Question 10ChallengeHigher

Expand and simplify $(x + 2)(x - 1)(2x + 3)$

Question 11ChallengeHigher

Expand and simplify $(n + 3)^2 - (n - 3)^2$ . What does your answer show about this expression when $n$ is a whole number?

Question 15ChallengeHigher

Expand and simplify $2(x + 3)^2 - (x + 1)(x - 4)$

Common mistakes

Writing (x − 3)² as x² + 9 or x² − 9: it's x² − 6x + 9.
Multiplying only the first term inside the bracket: 5(x − 3) is 5x − 15, not 5x − 3.
Sign errors with negatives: −2(x − 4) = −2x + 8.
Missing one of the four products in a double bracket.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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