### Introduction

In this Section we explain what is meant by the phrase ‘like terms’ and show how like terms are collected together and simplified.

Next we consider removing brackets. In order to simplify an expression which contains brackets it is often necessary to rewrite the expression in an equivalent form but without any brackets. This process of removing brackets must be carried out according to particular rules which are described in this Section.

Finally, factorisation, which can be considered as the reverse of the process, is dealt with. It is essential that you have had plenty practice in removing brackets before you study factorisation.

#### Prerequisites

- be familiar with algebraic notation
- have competence in removing brackets

#### Learning Outcomes

- use the laws of indices
- simplify expressions by collecting like terms
- use the laws of indices
- identify common factors in an expression
- factorise simple expressions
- factorise quadratic expressions

#### Contents

1 Addition and subtraction of like terms2 Removing brackets from expressions $a\left(b+c\right)$ and $a\left(b-c\right)$

3 Removing brackets from expressions of the form $\left(a+b\right)\left(c+d\right)$

4 Engineering Example 1

4.1 Reliability in a communication network

5 Factorisation

6 Factorising quadratic expressions

6.1 Case 1

6.2 Case 2