Factorise ab + ac
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Factorise expressions by finding common factors.

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to how to factorise expressions by finding common factors.   
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Algematics software. Click here for instructions.


Factorising an algebraic expression is the opposite of expanding. You start with a sum or difference of terms and finish up with a product.

For example, if you factorise:

ab + ac

you get:

a(b + c)

You can factorise a sum or difference of terms by the common factor method if there is at least one common factor other than 1 between all the terms.

In the example, all terms have ‘a’ as a factor, so ‘a’ is a common factor.

Once all common factors have been identified, you write them down as the factors that go outside the brackets.

In the example, the only common factor is 'a', so this will be the only factor outside the brackets:

a(      +      )

To find out what goes inside the brackets, divide the original terms by the common factor(s).

For the example, divide the original terms by ‘a’:

ab ¸ a = b,

ac ¸ a = c,

The last step is to write these new expressions inside the brackets, like this:

a( b  +  c )

The factorising process is more difficult when numbers and powers are involved, because finding the common factors requires more work. 

The steps below describe how to use Algematics to factorise even the most difficult of these expressions.

Download the free support file... We have created an Algematics document containing the completed example from this topic. It also includes practice exercises to improve your skills.

File name:  'Factorise1.alg'   File size: 2kb
Click here
to download the file.

If you choose 'Open this file from its current location', then Algematics should open the document immediately. If not, try the other option: 'Save this file to disk', then run Algematics and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Algematics installed on your computer, click here for instructions.


IMPORTANT: This topic assumes that you know how to enter mathematical formulas into Algematics. Find out how by completing the three simple tutorials in the 'Getting Started' section of the Algematics program 'Help'.

Algematics has a factorise command that will examine an algebraic expression and try many different techniques to factorise the expression or sub-expressions within it.  Sometimes several factorising steps are possible, but the first step is always to look for common factors. Because of this, you will only need to use the factorise command once in order to take common factors outside the brackets.

Step1  Enter the data

Click  and type the expression to be factorised into the maths box in the data entry dialog box.

If the ‘EMPTY’ message is not displayed between the blue buttons, click the  button until the message: ‘INSERT’ appears. If required, use the ‘ * ’ symbol for multiply, and the ‘ / ’ symbol for divide.



   ab + ac




and then click

Step 2  Factorise

·Â Â Â Â Â Â Â Â  Click  (factorise) once.

If the terms have common factors, the factorised expression will be written with the common factors to the left and the divided terms inside brackets as explained above.

The example will factorise like this:

a( b  +  c )

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