# Simplifying expressions

## Collecting like terms

Collecting like terms means to simplify terms in expressions in which the variables are the same. In the expression , the terms and are like terms, as are and .

### Example 1

Simplify .

Adding the four like terms together gives .

### Example 2

Simplify .

In this expression, all the terms are like terms as the variable in each term is . Simplify the expression in order:  Question

Simplify .

This expression contains three types of terms: the terms that contain c's, terms that contain d's and terms that are numbers alone.

To simplify this expression, collect the like terms.    This gives .

Question

Simplify .

This expression contains two types of different terms, those that contain and those that contain . and are not like terms because although they contain the same letter, the letters do not have the same .   Putting the simplified terms together gives .

If there is only one of the letter, like in the answer to , do not write the 1. A letter on its own means that there is only one of them, for example, .

## Using letters and numbers

Algebraic expressions can be added and subtracted by collecting like terms, but expressions can also be multiplied and divided.

### Example 1

Simplify .

Multiplying a number or letter by itself is called squaring. This means (read as 'a squared'). In , the 2 is known as the index number or power. Powers tell us how many times a number or letter has been multiplied by itself.

### Example 2

Simplify .

In this example, is being multiplied by itself three times. The power of will be three, so, .

Question

Simplify .

Multiply the numbers first. This gives . Then multiply .

The final answer is .

Question

Simplify .

Dividing the variable and the numbers separately gives and , so simplified is .