Fiducia TogetherFactorising
Putting an expression back into brackets. The reverse of expanding.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
Factorising writes an expression as a product: 6x + 9 becomes 3(2x + 3); x² + 5x + 6 becomes (x + 2)(x + 3).
Where it applies
Both tiers. Higher adds factorising quadratics where the x² coefficient is not 1, and the difference of two squares.
How it works
For a quadratic x² + bx + c, find two numbers that multiply to c and add to b.
The difference of two squares, a² − b² = (a + b)(a − b), is worth recognising on sight because it appears constantly.
Always take out a common factor first.
How to use it in your work
Check by expanding your answer. It takes ten seconds and catches almost every error.
When a question says "factorise fully", one bracket is rarely the whole answer.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.