IGCSE Math RevisionQuestion 1
Multiply out the brackets and collect like terms: \(4(3x - 2) - 3(x - 5)\).
Show the worked answer
- \(4(3x - 2) = 12x - 8\) and \(-3(x - 5) = -3x + 15\).
- \(12x - 8 - 3x + 15 = 9x + 7\)
Answer: \(9x + 7\)
Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.2
Cambridge IGCSE Maths 0580 Expanding and Factorising Questions
Expanding and Factorising questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 11 questions
- 6 Core
- 5 Extended
- 9 non-calculator
- Free, no sign-in
What the syllabus asks
- 2.2 Algebraic manipulation Core Extended
Simplify by collecting like terms; Expand products of algebraic expressions, including two brackets in one variable, e.g. (2x + 1)(x − 4); Factorise by taking out common factors.
Extended also: Expand products of more than two brackets; Factorise expressions such as ax + bx + kay + kby, a²x² − b²y², a² + 2ab + b², ax² + bx + c and ax³ + bx² + cx; Complete the square.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Expanding and Factorising questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
Factorise fully \(15a^2b - 10ab^2\).
Show the worked answer
- The highest common factor of the terms is \(5ab\).
- \(15a^2b \div 5ab = 3a\) and \(10ab^2 \div 5ab = 2b\).
Answer: \(5ab(3a - 2b)\)
Question 3
Factorise
(a) \(6x + 15\) (b) \(x^2 - 7x\)
Show the answer and mark scheme
- B1 (a) 3(2x + 5)
- B1 (b) x(x − 7)
Answer: (a) \(3(2x + 5)\) (b) \(x(x - 7)\)
Question 4
Expand and simplify \((x + 7)(x - 3)\).
Show the worked answer
- \(x \times x = x^2\), \(x \times (-3) = -3x\), \(7 \times x = 7x\), \(7 \times (-3) = -21\)
- \(x^2 - 3x + 7x - 21 = x^2 + 4x - 21\)
Answer: \(x^2 + 4x - 21\)
Question 5
Expand and simplify \((x + 4)(x - 3)\).
Show the answer and mark scheme
- M1 at least three of x², −3x, +4x, −12
- A1 x² + x − 12
Answer: \(x^2 + x - 12\)
Question 6
Expand and simplify \((3x - 2)(x + 5)\).
Show the answer and mark scheme
- M1 at least three of 3x², 15x, −2x, −10
- A1 3x² + 13x − 10
Answer: \(3x^2 + 13x - 10\)
Expanding and Factorising questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 7
Write \(x^2 - 2x - 35\) as the product of two brackets.
Show the worked answer
- Find two numbers that multiply to \(-35\) and add to \(-2\): \(-7\) and \(5\).
Answer: \((x - 7)(x + 5)\)
Question 8
Factorise \(4x^2 - 49\).
Show the worked answer
- This is a difference of two squares: \((2x)^2 - 7^2\).
- \(a^2 - b^2 = (a + b)(a - b)\)
Answer: \((2x + 7)(2x - 7)\)
Question 9
Factorise \(2ax - 6a + bx - 3b\).
Show the worked answer
- Group in pairs: \(2a(x - 3) + b(x - 3)\).
- \((x - 3)\) is a common factor.
Answer: \((x - 3)(2a + b)\)
Question 10
Factorise \(5x^2 + 13x - 6\).
Show the worked answer
- \(5 \times (-6) = -30\). Two numbers that multiply to \(-30\) and add to \(13\): \(15\) and \(-2\).
- \(5x^2 + 15x - 2x - 6 = 5x(x + 3) - 2(x + 3) = (5x - 2)(x + 3)\)
Answer: \((5x - 2)(x + 3)\)
Question 11
Expand and simplify \((x + 2)(x - 1)(2x + 3)\).
Show the worked answer
- \((x + 2)(x - 1) = x^2 + x - 2\)
- \((x^2 + x - 2)(2x + 3) = 2x^3 + 3x^2 + 2x^2 + 3x - 4x - 6\)
- \(= 2x^3 + 5x^2 - x - 6\)
Answer: \(2x^3 + 5x^2 - x - 6\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Algebra and graphs practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Algebra and graphs revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test expanding and factorising?
Expanding and Factorising is on both tiers (syllabus 2.2), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more expanding and factorising questions?
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.