# Expanding brackets

Expanding brackets means multiplying everything inside the bracket by the letter or number outside the bracket. For example, in the expression both and 7 must be multiplied by 3:

.

Expanding brackets involves using the skills of simplifying algebra. Remember that and .

Expand .

Question

Expand .

Question

Expand .

## Expanding brackets with powers

Powers or index numbers are the floating numbers next to terms that show how many times a letter or number has been multiplied by itself. For example, and .

Using index laws, terms that contain powers can be simplified. Remember that multiplying indices means adding the powers. For example, .

### Example

Expand the bracket .

Multiply by first. and , so .

Then multiply by . and , so .

So, .

Question

Expand the bracket .

Multiply by . .

Multiply by . .

Multiply by . .

## Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, . In these cases first expand the bracket and then collect any like terms.

### Example 1

Expand and simplify .

### Example 2

Expand and simplify .

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives:

Collecting the like terms gives .

Answers are usually written with descending order of powers.