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 might be a letter. Today we are going to look at expressions where a common factor is a number.

Here's a typical question on this topic:

Factorise 12x - 18y.

Look at the numbers. We need to find the highest common factor of 12 and 18.

The factors of 12 are 1, 2, 3, 4, 6, 12.

The factors of 18 are 1, 2, 3, 6, 9, 18.

The highest factor which they have in common is 6, so 6 goes outside of the bracket.

6( __ __ )

Now we need to work out the inside of the bracket.

6 × 2x = 12x, so we need to put 2x in the bracket

6 × -3y = -18y, so we need to put -3y in the bracket

The final answer is 12x - 18y = **6(2x - 3y).**