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What do you need to do if you are asked to expand a single bracket in maths?

Updated on September 28, 2011


To expand a single bracket in math all you need to do is multiply the term on the outside of the bracket by the terms inside the bracket. It’s important that you know how to expand a bracket so that you can simplify expressions or solve harder equations. A couple of things to remember when expanding brackets are:

1) Make sure the letters are in alphabetical order, for example, 3d × 5c = 15cd

2) If you multiply a letter by itself it will become squared, for example, 7y × 3y = 21y²

Let’s take a look at a few examples that involve expanding brackets:

Example 1

Expand the bracket 6(2a + 3)

The 6 has to multiply both terms inside the bracket:

6 × 2a = 12a

6 × 3 = 18

So if you put these together on one line your final expression will be:

12a + 18

Example 2

Expand the bracket 4(9x + 3)

The 4 has to multiply both terms inside the bracket:

4 × 9x = 36x

4 × 3 = 12

So if you put these together on one line your final expression will be:

36x + 12

Example 3

Expand the bracket 7(6y - 4p)

The 7 has to multiply both terms inside the bracket:

7 × 6y = 42y

7 × -4p = -28p

So if you put these together on one line your final expression will be:

42y – 28p

Example 4

Expand the bracket 8d(3e + 5a)

This time you have 8d at the front of the bracket and this term must multiply both terms inside the bracket:

8d × 3e = 24de

8d × 5a = 40ad

So if you put these together on one line your final expression will be:

24de + 40ad

Example 5

Expand the bracket x(7x - y)

This time you have x at the front of the bracket and this term must multiply both terms inside the bracket:

x × 7x = 7x²

x × -y =- xy

So if you put these together on one line your final expression will be:

7x² -xy

Example 6

Expand the bracket 3x(2x + 7y)

This time you have 3x at the front of the bracket and this term must multiply both terms inside the bracket:

3x × 2x = 6x²

3x × 7y =21xy

So if you put these together on one line your final expression will be:

6x² + 21xy

Example 7

Expand the bracket 9d(d – 7de)

This time you have 9d at the front of the bracket and this term must multiply both terms inside the bracket:

9d × d = 9d²

9d × -7de = -63d²e

So if you put these together on one line your final expression will be:

9d² -63d²e

Example 8

Expand the bracket 5y(2x + y – 8z)

This time you have 5y at the front of the bracket and this term must multiply all of the 3 terms inside the bracket:

5y × 2x = 10xy

5y × y = 5y²

5y × -8z = -40yz

So if you put these together on one line your final expression will be:

10xy + 5y² - 40yz

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