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.