Where can I download free triple brackets PDF worksheets with answers?

On this MathsLinks page you can download free printable triple brackets PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page triple brackets revision guide.

What GCSE grade is triple brackets (6E)?

Triple brackets (topic code 6E) is a Grade 6 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Triple brackets Worksheets (PDF) with Answers — GCSE Maths

Free Triple brackets PDF Worksheets & Answers

Grade 6 • Topic 6E

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Maths4EveryOne Structured worksheet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 6 topics
6A - Recurring decimals	6B - Harder indices
6C - The product rule	6D - Repeated change
6E - Triple brackets	6F - Parallel and perpendicular
6G - Inequalities on graphs	6H - Similar shapes (area and vol)
6J - Negative scale factors	6K - Circle theorems
6L - Cumulative frequency	6M - Box plots
6N - Combined transformations	6P - Capture recapture

Explanation:

To expand three brackets (x + a)(x + b)(x + c), break the problem into two clear stages: first expand and simplify any two of the brackets into a single quadratic expression (x² + px + q).

Next, multiply every term in your simplified quadratic by every term in the third bracket (giving 6 terms before simplifying), then collect like terms in order: x³, x², x, and the number term.

Example 1: Expand and simplify (x + 3)(x − 2)(x + 5).

Solution:

Expand first two: (x + 3)(x − 2) = x² + x − 6

Multiply by (x + 5): x(x² + x − 6) + 5(x² + x − 6)

= x³ + x² − 6x + 5x² + 5x − 30

Collect like terms:

Answer: x³ + 6x² − x − 30

Example 2: Expand and simplify (2x − 1)(x + 4)(x − 3).

Solution:

Expand last two: (x + 4)(x − 3) = x² + x − 12

Multiply by (2x − 1): 2x(x² + x − 12) − 1(x² + x − 12)

= 2x³ + 2x² − 24x − x² − x + 12

Collect like terms:

Answer: 2x³ + x² − 25x + 12

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Triple brackets Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Nov 2023 2H Q16 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

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

Worked Solution & Mark Scheme (3 marks)

(2x + 3)(x² − x − 20) = 2x³ − 2x² − 40x + 3x² − 3x − 60 = 2x³ + x² − 43x − 60. M2 A1

Answer: 2x³ + x² - 43x - 60

Past Paper Example 2 GCSE Nov 2021 2H Q12 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

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

Worked Solution & Mark Scheme (3 marks)

(x – 2)(3x + 2) = 3x² – 4x – 4. (3x² – 4x – 4)(2x + 3) = 6x³ + 9x² – 8x² – 12x – 8x – 12 = 6x³ + x² – 20x – 12 M2 A1

Answer: 6x³ + x² - 20x - 12

Past Paper Example 3 GCSE May 2024 1H Q14 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Expand and simplify (3x - 1)(2x + 3)(x - 5)

Worked Solution & Mark Scheme (3 marks)

(3x – 1)(2x + 3) = 6x² + 7x – 3. Multiplying by (x – 5): 6x³ – 30x² + 7x² – 35x – 3x + 15 = 6x³ – 23x² – 38x + 15. M2 A1

Answer: 6x³ - 23x² - 38x + 15

← 6D Repeated change

Back to GCSE questions by topic

6F Parallel and perpendicular →

Triple brackets

Free Triple brackets PDF Worksheets & Answers

Guide to Triple brackets: Explanation, Diagrams & Worked Examples

GCSE Past Paper Triple brackets Questions & Answers