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 - 15x².

Answer

The HCF of 10x and 15x² is 5x.

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

The answer is 5x(2 - 3x)

We can check this by multiplying out the brackets again!

5x x 2 = 10x

5x x 3x = 15x²

So we get 10x - 15x²

Which is correct!

Let's make a start on some questions now.