How to Expand Brackets (Mathematics Lesson)
Expanding Brackets
Expanding brackets means multiplying terms to remove brackets from an expression.
Imagine we wanted to remove the brackets from the expression below. We have to expand the brackets.
How to Expand Brackets
Expanding brackets is easy.
Multiply each term inside the bracket with the term outside of the bracket.
An Example Question
Expand the brackets below.
Multiply the first term inside the bracket (x) with the term outside the bracket (2).
2x
Multiply the second term inside the bracket (1) with the term outside the bracket (2), and add to the previous result.
2x + 2
Expanding 2(x + 1) gives 2x + 2.
A Formula to Expand Brackets
The formula below shows how to expand brackets:
a, b and c stand in for any number or term.
A Real Example of How to Expand Brackets
The slider below shows another real example of how to expand brackets. In this example, there are more than two terms inside the brackets.
Curriculum
Interactive Test
showHere's a second test on expanding brackets.
Here's a third test on expanding brackets.
Note
Multiplication Tips

Multiplying a number with a variable
2 × x = 2x
5 × x = 5x 
Multiplying a number with a variable with a coefficient
2 × 2x = 4x
3 × 5x = 15x 
Multiplying a variable with a variable
x × y = xy
x × x = x^{2}
Be Careful With Signs
Each term in a bracket will have a sign.

positive terms have a + sign in front of them, or no sign if it is the first term.

negative terms have a − sign in front of them.
These signs must be included when multiplying terms.
Remember the rules for multiplying different signs:
Same signs give a plus:
Different signs give a minus: