Where can I download free expanding and factorising PDF worksheets with answers?

On this MathsLinks page you can download free printable expanding and factorising PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), Maths Genie, Corbett Practice, Corbett Textbook, plus a printable one-page expanding and factorising revision guide.

What GCSE grade is expanding and factorising (4J)?

Expanding and factorising (topic code 4J) is a Grade 4 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Expanding and factorising Worksheets (PDF) with Answers — GCSE Maths

Free Expanding and factorising PDF Worksheets & Answers

Grade 4 • Topic 4J

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked 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
Hannah Kettle Practice sheet & answers	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket (1) Practice questions & answers	Qs	Ans
GCSE Maths Rocket (2) Practice questions & answers	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Metatutor (1) Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket (3) 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 4 topics
4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction

Explanation:

To expand a single bracket, multiply the term outside the bracket by every term inside the bracket. When expanding and simplifying two separate brackets, be careful with a negative sign in front of the second bracket (e.g. −2(x − 3) = −2x + 6).

Factorising is the reverse of expanding: find the highest common factor (HCF) of the numbers and the letters, write it outside a bracket, and divide each term by that HCF to find what goes inside. Check by expanding back out.

Example 1: Expand and simplify 4(2x + 3) − 3(x − 5)

Solution:

Expand 1st bracket: 4(2x + 3) = 8x + 12

Expand 2nd bracket: −3(x − 5) = −3x + 15

Collect like terms: 8x − 3x + 12 + 15

Answer: 5x + 27

Example 2: Factorise fully 12x²y − 18xy³

Solution:

HCF of 12 and 18 is 6.

Common letters: xy → full HCF = 6xy

Divide each term by 6xy: 2x and −3y²

Answer: 6xy(2x − 3y²)

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Expanding and factorising Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE May 2019 1F Q16 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Expand 5(2m – 3) (1) (b) Factorise 3n + 12 (1)

(a) Expand 5(2m - 3) [1 mark]

(b) Factorise 3n + 12 [1 mark]

Worked Solution & Mark Scheme (2 marks)

Part (a) Solution:

5 × 2m – 5 × 3 = 10m – 15 B1

Answer (a): 10m - 15

Part (b) Solution:

3(n + 4)

Answer (b): 3(n + 4)

Past Paper Example 2 GCSE Nov 2017 3F Q17 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Factorise 4m + 12. (1) (b) Complete: 5y is a [term] in the [expression] 3x + 5y. (2)

(a) Factorise 4m + 12 [1 mark]

(b) Choose two words from the box above to make this statement correct. [2 marks]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

4(m + 3)

Answer (a): 4(m + 3)

Part (b) Solution:

5y is a term in the expression 3x + 5y M1 A1

Answer (b): term, expression

Past Paper Example 3 GCSE Nov 2024 2F Q19 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Factorise fully 15w² – 5w (2)
(b) On the number line, show –2 < x ⩽ 4 (2)

(a) Factorise fully 15w² - 5w [2 marks]

(b) On the number line below, show the set of values of x for which –2 < x ≤ 4 [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

Difference of two squares: a² - b² = (a + b)(a - b) M1
e.g. m² - 9 = (m + 3)(m - 3)
Answer: 5w(3w - 1) A1

Answer (a): 5w(3w - 1)

Part (b) Solution:

Open circle at –2, closed circle at 4, joined by a line M1 A1

Answer (b): Open circle at –2, closed circle at 4, joined by a line

← 4H nth term of a linear sequence

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Expanding and factorising

Free Expanding and factorising PDF Worksheets & Answers

Guide to Expanding and factorising: Explanation, Diagrams & Worked Examples

GCSE Past Paper Expanding and factorising Questions & Answers