Expanding Double Brackets Questions with Answers

Free maths practice · Skills Lab

Expanding Double Brackets Questions with Answers

Here are 18 expanding double brackets questions with answers, split into 9 levels that start with (x + 3)(x + 5) and build up to squared brackets, coefficients and brackets with three terms. For a fresh set of 10 questions at any level, open the same skill in our free Skills Lab, which also steps through the working one line at a time.

  • 9levels, easiest first
  • 18questions on this page, with answers
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Skills Lab teach mode working through expanding double brackets step by step
Teach: the working, one step at a timeArrows show which two terms are being multiplied, so your child sees every product before the like terms are collected.
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How to expand double brackets

Multiply every term in the first bracket by every term in the second bracket, keeping each sign with its term. Then collect the like terms. A grid helps: write one bracket along the top, the other down the side, and fill in each box.

Expand (x + 3)(x − 5)

  1. x × x = x², x × −5 = −5x
  2. 3 × x = 3x, 3 × −5 = −15
  3. x² − 5x + 3x − 15 = x² − 2x − 15

Expand (x + 4)²

  1. Write it as two brackets: (x + 4)(x + 4)
  2. x² + 4x + 4x + 16
  3. x² + 8x + 16

Expanding Double Brackets Questions by level

Click a level to practise it
Level Question Question
Level 1Two brackets 1. (a + 11)(a + 3) 2. (f + 10)(f + 2)
Level 2Two brackets, with negatives 3. (n + 4)(n − 12) 4. (h − 8)(h + 8)
Level 3A bracket squared 5. (u + 12)² 6. (f + 12)²
Level 4Squared, with negatives 7. (u − 14)² 8. (b − 4)²
Level 5A coefficient in front of the letter 9. (5b + 9)² 10. (6g − 3)(6g + 6)
Level 6Coefficients and negatives 11. (−4u + 9)² 12. (7x + 7)(−4x + 12)
Level 7Three terms in a bracket 13. (q² + 9q + 8)(q² + 9q + 4) 14. (x² + 7x + 7)(x² + 4x + 7)
Level 8Three terms, negatives and coefficients 15. (4q² − 9q + 1)² 16. (2w² + 6w − 3)(6w − 7)
Level 9Everything mixed 17. (k² + 5k + 3)² 18. (h + 12)(4h + 8)
Show all 18 answers
Question Answer
1. (a + 11)(a + 3) a² + 14a + 33
2. (f + 10)(f + 2) f² + 12f + 20
3. (n + 4)(n − 12) n² − 8n − 48
4. (h − 8)(h + 8) h² − 64
5. (u + 12)² u² + 24u + 144
6. (f + 12)² f² + 24f + 144
7. (u − 14)² u² − 28u + 196
8. (b − 4)² b² − 8b + 16
9. (5b + 9)² 25b² + 90b + 81
10. (6g − 3)(6g + 6) 36g² + 18g − 18
11. (−4u + 9)² 16u² − 72u + 81
12. (7x + 7)(−4x + 12) −28x² + 56x + 84
13. (q² + 9q + 8)(q² + 9q + 4) q⁴ + 18q³ + 93q² + 108q + 32
14. (x² + 7x + 7)(x² + 4x + 7) x⁴ + 11x³ + 42x² + 77x + 49
15. (4q² − 9q + 1)² 16q⁴ − 72q³ + 89q² − 18q + 1
16. (2w² + 6w − 3)(6w − 7) 12w³ + 22w² − 60w + 21
17. (k² + 5k + 3)² k⁴ + 10k³ + 31k² + 30k + 9
18. (h + 12)(4h + 8) 4h² + 56h + 96

Common mistakes

  • Squaring each term on its own. (x + 4)² is not x² + 16. Write out both brackets and you will see the middle term, 8x.
  • Losing a minus sign. The sign belongs to the term after it. In (x + 3)(x − 5), the last term is 3 × −5 = −15.
  • Not collecting like terms at the end. x² − 5x + 3x − 15 is correct but not finished. Collect −5x + 3x to get −2x.

Questions parents and students ask

What is the quickest way to expand double brackets?

Use a grid or FOIL (first, outside, inside, last). Both make sure every term in one bracket multiplies every term in the other.

How do you expand a bracket squared?

Write the bracket twice and expand as normal: (x − 3)² = (x − 3)(x − 3) = x² − 6x + 9.

Is expanding double brackets on GCSE Foundation?

Yes. Expanding two brackets like (x + 2)(x + 5) is on both Foundation and Higher. Higher adds three brackets and harder coefficients.

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