# Expanding Brackets(KS3, Year 7)

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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 brackets with the term outside of the bracket.

## Question

Expand the brackets below.

## 1

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

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 × 1 = 2

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.

## 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

## Be Careful with Signs

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

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