GCSE-readyExpanding three brackets
Three brackets are just two steps of something you already know: expand two of them, then multiply by the third.
Two, then the third
First: (x + 1)(x + 2) = x2 + 3x + 2
Then: (x2 + 3x + 2)(x + 3)
Each of the 3 terms times each of the 2 terms gives 6 terms.
= x3 + 3x2 + 3x2 + 9x + 2x + 6 = x3 + 6x2 + 11x + 6
Negatives and coefficients
(2x + 1)(x − 3) = 2x2 − 5x − 3
(2x2 − 5x − 3)(x + 2) = 2x3 − x2 − 13x − 6
Keep each sign with the term after it.
Cubes and checking
Check with x = 1: (1 + 2)3 = 27 and 27 from the expansion. They match.
Expand and simplify (x − 1)(x + 4)(x − 2).
- (x − 1)(x + 4) = x2 + 3x − 4
- (x2 + 3x − 4)(x − 2)
- = x3 + x2 − 10x + 8
Answer: x3 + x2 − 10x + 8
Expand two brackets, simplify, then multiply every term by every term in the third bracket. Check by putting x = 1 into both forms.
Try two quick questions
See if it has sunk in. Answers are marked straight away.
2 more questions
Try each one, then tap to check.
Find the coefficient of x2 in the expansion of (x + 6)(x − 5)(x − 6).
Show the answer
Answer: -5
The full expansion is x3 − 5x2 − 36x + 180, so the coefficient of x2 is −5.
Before collecting like terms, how many terms do you get from (x + a)(x + b)?
- 2
- 3
- 4
- 6
Show the answer
Answer: 4
2 terms × 2 terms = 4 products.
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- Pearson Edexcel GCSE Mathematics (1MA1) specification, topic A4
- Pearson Edexcel International GCSE Mathematics (4MA1) specification, topic 2.2
Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.