Expanding Brackets
(KS3, Year 7)

The Lesson

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 brackets with the term outside of the bracket.

Question

Expand the brackets below.
2 ( x plus 1 )

Step-by-Step:

1

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

2 times x
2 × x = 2x 2x

2

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

2 times 1
2 × 1 = 2 2x + 2

Answer:

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.

Lesson Slides

The slider below shows another real example of how to expand brackets. In this example, there are more than two terms inside the brackets. Open the slider in a new tab

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

Beware

Be Careful with Signs

Each term in the brackets 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
Help Us To Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form

See Also

What is algebra? What is a term? What is an expression? Multiplying letters Multiplying terms