Edexcel IGCSE 4MA1 Expanding and Factorising: Exam Questions

Edexcel IGCSE 4MA1 Expanding and Factorising: Exam Questions and Answers

Expanding and Factorising questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 4 worked examples first, then cover each solution and redo it yourself.

4 worked examples

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Start with one question on factorising quadratics. Stuck? Take a hint. No sign-in needed.

Factorise

x^{2} + 5 x - 14

Choose your answer · keys 1–4

(x - 14) (x + 5)

(x - 2) (x + 7)

(x - 14) (x + 1)

(x - 7) (x + 2)

What this topic covers

Expanding brackets & factorising: Multiplying out brackets and reversing the process to factorise expressions.
Brackets 1: Expanding a single bracket.
Brackets 2: Expanding two brackets (FOIL).
Brackets 3: Expanding three brackets or a squared bracket.

Expanding and Factorising worked examples

Worked example 1: Expanding double brackets

Expand and simplify $(x + 4) (x - 6)$ .

Solution

Multiply each term in the first bracket by each term in the second: $x^{2} - 6 x + 4 x - 24$ .
Collect like terms: $x^{2} - 2 x - 24$ .

3 steps

Tip: Four terms before collecting, three after.

Worked example 2: Single brackets

(a) Expand $5 (2 x - 3)$ . (b) Factorise $8 x + 20$ .

Solution

(a) $5 \times 2 x - 5 \times 3 = 10 x - 15$ .
(b) HCF of 8 and 20 is 4: $4 (2 x + 5)$ .

3 steps

Tip: Factorising is the reverse of expanding; check by expanding back.

Worked example 3: Double brackets

Expand and simplify $(3 x + 2) (x - 4)$ .

Solution

$3 x \times x = 3 x^{2}$ , $3 x \times - 4 = - 12 x$ , $2 \times x = 2 x$ , $2 \times - 4 = - 8$ .
Collect: $3 x^{2} - 10 x - 8$ .

3 steps

Tip: A grid method helps keep track of all four products.

Worked example 4: Triple brackets

Expand $(x + 1) (x + 2) (x + 3)$ .

Solution

First two brackets: $x^{2} + 3 x + 2$ .
Multiply by $(x + 3)$ : $x^{3} + 3 x^{2} + 3 x^{2} + 9 x + 2 x + 6$ .
Collect: $x^{3} + 6 x^{2} + 11 x + 6$ .

4 steps

Tip: Expand two brackets first, then the third.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Questions students ask

Which Edexcel IGCSE Maths papers test expanding and factorising?

Either Higher tier paper, 1H or 2H, can test expanding and factorising: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more expanding and factorising questions?

In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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Edexcel IGCSE 4MA1 Expanding and Factorising: Exam Questions and Answers

Try it first

What this topic covers

Expanding and Factorising worked examples

Worked example 1: Expanding double brackets

Solution

Worked example 2: Single brackets

Solution

Worked example 3: Double brackets

Solution

Worked example 4: Triple brackets

Solution

Revise expanding and factorising for the exam

Questions students ask

Practise expanding and factorising with your progress saved

More Unit 2 topics: Algebra Basics