Factorising Expressions

Depending on the question, sometimes we want to expand brackets, and sometimes we want to do precisely the opposite and put our term into brackets. This is called factorising and means that we are rewriting our expression as a product.

To do it we need to get skilful at spotting common factors in terms. These are numbers (or letters) that every term can be divided by.

Can you spot the common factor in 6x + 12 – 3y ?

So can you factorise it?

How about in 10x – 5x² +30xy?

Sometimes we can do this process twice.

Consider factorising this expression: 10 + 2x – 5y – xy.

Let’s try some together:

Now try this exercise on your own (from exercises 2E and 2F on pages 25 and 26 of the textbook):

Below are the answers to the questions in the above exercise: