The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Expand a Single Bracket

In this worksheet, students will expand single brackets.

'Expand a Single Bracket' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Expanding brackets means removing brackets by multiplying everything inside of the bracket by what is just outside of the bracket.

Let's have a look at a few examples.

 

Expand 3(4x − 2)

We will multiply 3 by 4x and 3 by −2

3 × 4x = 12x

3 × −2 = −6

Now we put these together to get the final answer: 12x − 6

 

 

Expand

−5(7 − 5b)

We will follow the same method, but we need to be careful with the negative sign.

−5 × 7 = −35

−5 × − 5b = 25b (positive!)

So the answer is −35 + 25b

 

Remember:

  • when we multiply a negative by a positive number, the answer is negative
  • when we multiply two negative numbers, the answer will be positive.

Expand 2(x+5)

Expand 3(2x + 4)

Expand 7(3p - 2q)

Lisa and Ruby expand 4(3a - 5b).

Lisa says the answer is 12a - 5b.

Ruby says that the answer is 12a - 20b.

Who is correct?

Lisa

Ruby

Neither

Can you spot the mistake here?

2(4y + 3)

2 × 4y = 8y

2 × 3 = 5

2(4y + 3) = 8y + 5

Underline where you think the mistake first appeared.

2(4y + 3) 2 × 4y = 8y 2 × 3 = 5 2(4y + 3) = 8y + 5

Can you spot the mistake here?

2(w - 5)

2 × 2 = 2w

2 × 5 = 10

2(w - 5) = 2w 10

Underline where you think the mistake first appeared.

−2(w - 5) −2 × 2 = −2w −2 × −5 = −10 −2(w - 5) = −2w − 10

−5(3x + 1) = −15x + 1

True

False

Find the expression for the area of the area of the composite shape below.

Give you answer in a simplified form.

 

A rectangle has a width of 6cm and a length of (x + 7)cm.

What is the area of this rectangle?

Give you answer in a simplified form.

Find the area of a parallelogram with the length of xy cm and the width of (4xy -1)cm.

  • Question 1

Expand 2(x+5)

CORRECT ANSWER
2x+10
2x + 10
EDDIE SAYS
Remember to multiply everything inside of the bracket by what is outside of it. This will give us: 2 × x = 2x and 2 × 5 = 10 So we get 2x + 10 as an answer. Have a go at another question now.
  • Question 2

Expand 3(2x + 4)

CORRECT ANSWER
6x + 12
6x+12
6x+ 12
EDDIE SAYS
Did you follow the method? 3 × 2x = 6x 3 × 4 = 12 So the answer is 6x +12.
  • Question 3

Expand 7(3p - 2q)

CORRECT ANSWER
21p - 14q
21p-14q
21p- 14q
EDDIE SAYS
This one looks a little more difficult, but we just need to follow the same method. 7 × 3p = 21p 7 × -2q = -14q Put it back together and the answer is 21p - 14q.
  • Question 4

Lisa and Ruby expand 4(3a - 5b).

Lisa says the answer is 12a - 5b.

Ruby says that the answer is 12a - 20b.

Who is correct?

CORRECT ANSWER
Ruby
EDDIE SAYS
It looks like Lisa forgot to multiply 4 and -5b! Ruby is correct, because she multiplied out both terms in the bracket.
  • Question 5

Can you spot the mistake here?

2(4y + 3)

2 × 4y = 8y

2 × 3 = 5

2(4y + 3) = 8y + 5

Underline where you think the mistake first appeared.

CORRECT ANSWER
2(4y + 3)

2 × 4y = 8y

2 × 3 = 5

2(4y + 3) = 8y + 5
EDDIE SAYS
In the third line of their working, the student added 2 and 3 instead of multiplying 2 × 3.
  • Question 6

Can you spot the mistake here?

2(w - 5)

2 × 2 = 2w

2 × 5 = 10

2(w - 5) = 2w 10

Underline where you think the mistake first appeared.

CORRECT ANSWER
−2(w - 5)

−2 × 2 = −2w

−2 × −5 = −10

−2(w - 5) = −2w 10
EDDIE SAYS
Did you remember that a negative × a negative gives you a positive? This is why −2 × −5 = 10, so the answer should have been −2(w - 5) = −2w + 10
  • Question 7

−5(3x + 1) = −15x + 1

CORRECT ANSWER
False
EDDIE SAYS
Whoops! Somebody forgot that you also need to multiply −5 × 1. The correct answer would be −15x - 5.
  • Question 8

Find the expression for the area of the area of the composite shape below.

Give you answer in a simplified form.

 

CORRECT ANSWER
6x+12
6x + 12
6x+ 12
6 x + 12
EDDIE SAYS
This is a sort of question you might get in a GCSE exam, so don't worry if you are not 100% confident yet. The shape can be divided into two rectangles, the big one at the top and a small one at the bottom. Do you remember how to find area of a rectange? base × height So the area of the bigger rectangle is 4(x +3). You do know how to expand brackets now! 4(x + 3) = 4x + 12 The area of the smaller rectangle is x × 2 = 2x Now add these together and simplify 4x + 12 + 2x = 6x + 12
  • Question 9

A rectangle has a width of 6cm and a length of (x + 7)cm.

What is the area of this rectangle?

Give you answer in a simplified form.

CORRECT ANSWER
EDDIE SAYS
To find area of a rectangle, multiply width by length. 6 × (x + 7) = 6(x + 7) = 6x + 42 cm²
  • Question 10

Find the area of a parallelogram with the length of xy cm and the width of (4xy -1)cm.

CORRECT ANSWER
EDDIE SAYS
You find the are of a parallelogram in exactly the same way as the area of a rectangle: length × width. Your calculation should be xy × (4yx - 1) = xy(4xy - 1) xy × 4xy = 4x²y² xy × −1 = −xy So the area of this parallelogram is: 4x²y² −xy
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.