Expanding Brackets
(KS3, Year 7)

home▸sitemap▸algebra▸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 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

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.

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.

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