Expanding Triple Brackets — Practice Questions
12 exam-style questions (36 marks), building from warm-up to grade 8–9. Show full working: Edexcel gives method marks even when the final answer is wrong.
Section A — Warm-up (grades 4–5)
- (2 marks)Expand and simplify (x + 1)(x + 2)(x + 5).
- (3 marks)Expand and simplify (x + 4)(x − 2)(x + 1).
- (3 marks)Expand and simplify (x − 3)(x − 1)(x + 5).
- (3 marks)Expand and simplify (x + 2)³.
Section B — Core (grades 5–7)
- (3 marks)Expand and simplify (2x + 3)(x − 1)(x + 4).
- (3 marks)Expand and simplify (3x − 2)(2x + 1)(x − 4).
- (3 marks)Expand and simplify (2x − 5)³.
- (3 marks)Show that (x + 3)(x − 3)(2x + 1) = 2x³ + x² − 18x − 9.
- (3 marks)A cuboid has length (x + 1) cm, width (x + 2) cm and height (2x − 3) cm. Show that its volume, in cm³, is 2x³ + 3x² − 5x − 6.
Section C — Stretch (grades 8–9)
- (2 marks)Find the coefficient of x² in the expansion of (x + 2)(x − 5)(3x + 1), without expanding fully.
Hint
An x² term comes from choosing x from two brackets and the number from the third. - (4 marks)(x + a)(x − 4)(x + 1) ≡ x³ + bx² − 7x + c, where a, b and c are integers. Find a, b and c.
- (4 marks)(a) Show that (n + 1)³ − n³ = 3n² + 3n + 1.
(b) Hence prove that the difference between the cubes of two consecutive integers is always odd.
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