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Factorise Expressions Using the Laws of Indices

In this worksheet, students will factorise expressions using the laws of indices.

'Factorise Expressions Using the Laws of Indices' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:  

Worksheet Overview

In this activity, we are going to do the inverse of expanding out brackets.


We are going to practise factorising an expression.


girl and question marks


We need to remember the laws of indices!


When multiplying, we add the powers.

When dividing, we subtract the powers.



Let's look at a typical question.



Factorise fully: 

4a + 6a2



We look for the highest common factor of the terms:



We can see from above the highest common factor is 2a, so that is what will go on the outside of the bracket.


We do 4a ÷ 2a =           and      6a2 ÷ 2a = 3a


4a + 6a2 = 2a(2 + 3a)


It's always a good idea to check that it works by expanding the newly factorised expression!


It really is easier than it looks, so let's get started!


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