Factorise Expressions Using the Laws of Indices

In this activity, we are going to do the inverse of expanding out brackets.

We are going to practise factorising an expression.

We need to remember the laws of indices!

When multiplying, we add the powers.

When dividing, we subtract the powers.

Let's look at a typical question.

Example

Factorise fully: 

4a + 6a²

Answer

We look for the highest common factor of the terms:

We can see from above the highest common factor is 2a, so that is what will go on the outside of the bracket.

We do 4a ÷ 2a = 2            and      6a² ÷ 2a = 3a

4a + 6a² = 2a(2 + 3a)

It's always a good idea to check that it works by expanding the newly factorised expression!

It really is easier than it looks, so let's get started!