---
title: "Factorising Expressions"
description: "Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)"
canonical: https://lightmysky.com/learn/mathematics/factorising-expressions-mt_uESbzWCZIq
source: https://lightmysky.com/learn/mathematics/factorising-expressions-mt_uESbzWCZIq.md
retrieved: 2026-10-19
---

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# Factorising Expressions

Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

Subject: Mathematics · Area: Algebra · Ages 12 to 13
Page: https://lightmysky.com/learn/mathematics/factorising-expressions-mt_uESbzWCZIq

## Ready when they can

- Identify the highest common factor of all terms in an expression
- Write the factorised form as a product of the HCF and a bracket
- Check factorisation by expanding the brackets back out

## Lesson: Factorising by Taking Out a Common Factor

You already know how to expand brackets, turning something like 3(2x + 3) into 6x + 9. Factorising goes the other way. You start with 6x + 9 and rewrite it as 3(2x + 3).

To factorise, first find the highest common factor, or HCF, of every term. The HCF is the biggest number that divides evenly into all of them. For 6x + 9, that number is 3.

**Example.** Look at 6x + 9. The terms are 6x and 9. The biggest number that divides both 6 and 9 is 3. Divide each term by 3: 6x divided by 3 is 2x, and 9 divided by 3 is 3. Write the HCF outside a bracket with the results inside: 3(2x + 3).

*(drawing: The 6x term is 6 of something, and the 9 is 9 more. Both piles split neatly into threes, and that is why 3 can be taken out of every term in 6x + 9.)*

**Example.** Try 10x - 15. The highest common factor of 10 and 15 is 5. Dividing each term by 5 gives 2x and 3, so the factorised form is 5(2x - 3).

**Tip.** Always check your answer by expanding the brackets back out. If 3(2x + 3) really equals 6x + 9, your factorising is correct.

**Recap.** Find the biggest number that divides every term, write it outside a bracket, then check by expanding back out.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Expanding Single Brackets](https://lightmysky.com/learn/mathematics/expanding-single-brackets-mt_FX4a2Q8XXN)
- [Sign Rules for Multiplication and Division](https://lightmysky.com/learn/mathematics/sign-rules-for-multiplication-and-division-mt_rxInpOQ74w)

## Opens up

- [Factorising Quadratics into Two Brackets](https://lightmysky.com/learn/mathematics/factorising-quadratics-into-two-brackets-mt_3QXgmWKfoA)