# To understand factorising, you need to be confident with expanding

In mathematics, expanding is referring to the process of multiplying out any factorised expressions and to remove any brackets joining terms. As an example, let's take 3(x+2) as the expression. To expand this expression, we would multiply the 3 by x and then add to the 3 by 2. The expanded form would look like this:

3(x+2) = 3*x + 3*2 = 3x + 6

If you are not sure about this process, you should ask in our online classroom. To warm up, expand the following expressions before moving on to the factorising section.

1. 12(x + 5)

2. 20(2x + 3)

3. x(x+2)

## Factorising - Quick Guide

Factorising can be thought of as the opposite to expanding. So rather than removing all brackets in an expression, you will need to find common factors for each term and introduce new brackets. To begin, let's take a look at some examples of common factors.

6x and 2x - Highest common factor (HCF) of 2x

12y and 18y - HCF of 6y

To factorise then, you need to first take out the HCF from each term and place this beside a pair of brackets. Then place the remainder of each term within the brackets. To illustrate this, we shall consider the following:

**6x + 2x**.......HCF here is 2x, so this will be taken out from each term

**= 2x(_____)**.....HCF taken out and brackets inserted

**= 2x(3 + 1)**....6x = 2x*3 and 2x = 2x*1

This results in the factorised form of 6x + 2x. The same process can be followed for any expression that you need to factorise. For more help on any of this, please head over to the tutenow classroom.

For more practice or help, join our online classroom and meet with a tutor.