Factorising (Foundation) – GCSE Maths Revision and Worksheets

Welcome to an introduction to the GCSE Maths topic, factorising. If you are looking to revise the basics of factorising then the worksheets on this page are great. You will be able to revise how to factorise a single bracket and then you will have plenty of opportunity to practise factorising different algebra expressions with different powers. From the difference of two squares to factorising terms with multiple letters and equations, there is plenty to practise for this topic.

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What you need to know

What you need to know:

Factorising (putting things into brackets) is the opposite of expansion (taking things out of brackets). At the foundation level you are required to:

  • FACTORISE INTO A SINGLE BRACKET: a process which involves finding what all the terms in your expression have in common, and taking that outside a single bracket. This will look something like:

4a^2 + 6ab + 12a = 2a(2a + 3b + 6)

  • FACTORISE SIMPLE QUADRATICS: by a ‘simple quadratic’, we are referring to a quadratic equation of the form x^2 + bx + c, i.e. one where the coefficient of the x^2 term is never bigger than 1. In being asked to factorise a quadratic like this, you are required to understand the process of factorising it into two brackets by finding a pair of numbers which add to make b, the coefficient of x, and which multiply to make c, the constant. This will look something like:

x^2 + 4x + 3 = (x + 3)(x + 1)

You must also be able to recognise when a quadratic is the difference of two squares. This often occurs when the middle term (the x term) is missing in a quadratic. For example:

x^-9 factorises to (x + 3)(x - 3)

To those teachers and Maths tutors who are looking for high quality factorising materials then you have found the right site. The worksheets and factorising revision materials above are relevant to those starting their GCSE courses or for those who are studying foundation Maths. They are also great as starters and refreshers for those students who haven’t factorised in a while! You can find more great resources on our GCSE Maths revision page.

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