**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.