Follow Us on Twitter

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.

2 ( x plus 1 )

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.

2 ( x plus 1 )
Step 1

Multiply the first term inside the bracket (x) with the term outside the bracket (2).

2 times x
2 × x = 2x

2x

Step 2

Multiply the second term inside the bracket (1) with the term outside the bracket (2), and add to the previous result.

2 times 1
2 × 1 = 2

2x + 2

Expanding 2(x + 1) gives 2x + 2.

2 ( x plus 1 ) equals 2 x plus 2

A Formula to Expand Brackets

The formula below shows how to expand brackets:

a ( b plus c ) equals a b plus a c

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
Algebra Lessons
Interactive Test
  show
 

Here'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 = x2

Be Careful With Signs

Each term in a bracket will have a sign.

x plus 2 minus y
  • 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.

positive times positive and positive times negative

Remember the rules for multiplying different signs:

Same signs give a plus:

plus times plus equals plus. minus times minus equals plus

Different signs give a minus:

plus times minus equals minus. minus times plus equals minus