What do you need to do if you are asked to expand a single bracket in maths?
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
More help with brackets.
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