Expanding double brackets means multiplying terms in the pair of expressions to remove the brackets. Imagine we wanted to remove the brackets from the pair of expressions below. We have to expand the brackets.

## How to Expand Double Brackets

Expanding double brackets is easy.## Question

Expand the double brackets below.## Step-by-Step:

## 1

Write the

**first**term in the**first**brackets (x) in front of the**second**brackets (x + 2).**x(x + 2)**

## 2

Write the

**second**term in the**first**brackets (1) in front of the**second**brackets (x + 2), and add to the previous result.
x(x + 2)

**+ 1(x + 2)****Note:**The term is added because there is a**+**before the second term in the first brackets.## 3

Expand the

**first**single brackets,**x(x + 2)**.- Multiply the
**first**term inside the brackets (x) with the term outside the brackets (x).*x × x = x*^{2}**x**^{2}

- Multiply the
**second**term inside the brackets (2) with the term outside the brackets (x), and add to the previous result*x × 2 = 2x*x^{2}**+ 2x**

x(x + 2) = x

^{2}+ 2x## 4

Expand the

**second**single brackets,**1(x + 2)**.- Multiply the
**first**term inside the brackets (x) with the term outside the brackets (1).*1 × x = x***x**

- Multiply the
**second**term inside the brackets (2) with the term outside the brackets (1), and add to the previous result.*1 × 2 = 2*x

**+ 2**

1(x + 2) = x + 2

## 5

Replace the single brackets with their expansions.

## 6

Simplify the expression if necessary by collecting like terms together. In our example, we can collect the

**x**terms together.
x

^{2}**+ 2x + x**+ 2 = x^{2}**+ 3x**+ 2## Answer:

We have expanded the double 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 = x

^{2}

## Beware

## 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.**negative**terms have a**−**sign in front of them.

## You might also like...

algebra curriculumexpanding brackets using the grid methodunderstanding the FOIL methodsmultiplying expressions in algebra

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