Factorising is the reverse of multiplying out brackets.

We put an expression into brackets by taking out the highest common factor (HCF) of each term in the expression.

To work out what goes inside the brackets, we divide each term by this HCF.

Example

Factorise fully 10x - 15 + 25y

Answer

The HCF of 10x and 15 and 25y is 5.

So we take 5 outside the brackets and divide each term by 5 to work out what goes inside the brackets.

The answer is 5(2x - 3 + 5y)

We can do it backwards to check that it works:

5 x 2x = 10x

5 x -3 = -15

5 x 5y = 25y

Put them together to get 10x - 15 + 25y, so it works!!

Let's have a go at some questions.