Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Factorise Into a Single Bracket

In this worksheet, students will factorise expressions (i.e. add brackets in) by finding highest common factors in terms of numbers.

'Factorise Into a Single Bracket' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA,

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation Algebraic Expressions

Popular topics:   Factors worksheets

Difficulty level:  

Worksheet Overview

Factorising is the opposite of expanding brackets.

To factorise an expression, you need to look for a common factor.

It might be a number or a letter. 



Let's look at an example to see this in action.


e.g. Factorise 12x - 18y.


Look at the numbers.

We need to find the highest common factor (HCF) of 12 and 18.

The factors of 12 are: 1, 2, 3, 4, 6, 12, etc...

The factors of 18 are: 1, 2, 3, 6, 9, 18, etc...

The highest factor which they have in common is 6.


Place the number '6' goes outside of the bracket like this: 

6( __  _  __ )


Now we need to work out what goes inside of the bracket.

Remember we are aiming to writing an expression with exactly the same value as 12x - 18y.


6 × 2x = 12x, so we need to put 2x in the bracket.

6 × -3y = -18y, so we need to put -3y in the bracket.


So our final answer is:

12x - 18y = 6(2x - 3y)




In this activity, we will factorise expressions by finding highest common factors in terms of numbers.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started

Popular Maths topics

Try an activity or get started for free