 # Expand a Single Bracket

In this worksheet, students will expand one set of brackets in calculations and problems (i.e. multiply to remove them), expressing answers in their simplest forms. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation, Algebraic Expressions

Difficulty level:   ### 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 to see this in action.

e.g. Expand 3(4x − 2).

We will multiply 3 by 4x and 3 by −2.

3 × 4x = 12x

3 × −2 = −6

Now we put these elements back together to get our final answer:

12x − 6

e.g. Expand −5(7 − 5b).

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

−5 × 7 = −35

−5 × − 5b = 25b (positive!)

−35 + 25b

Remember:

When we multiply a negative by a positive number, our answer is negative.

When we multiply two negative numbers, our answer will be positive.

In this activity, we will expand one set of brackets in calculations and problems, expressing our answers in their simplest forms.

Expand:

2(x + 5)

Expand:

3(2x + 4)

Expand:

7(3p - 2q)

Lisa and Ruby both 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

Imagine that your friend's working is shown below.

The are trying to expand:

2(4y + 3)

Can you spot their mistake?

Underline where you think they first made a mistake.

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

Imagine that your friend's working is shown below.

The are trying to expand:

-2(w - 5)

Can you spot their mistake?

Underline where you think they first made a mistake.

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

True or false?

−5(3x + 1) = −15x + 1

True

False

Find the expression for the area of the composite shape below. A rectangle has a width of 6 cm and a length of (x + 7) cm.

What is the area of this rectangle?

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

Write the correct numbers and / or mathematical symbols in the blanks in the expression below.

• Question 1

Expand:

2(x + 5)

2x+10
2x +10
2x+ 10
2x + 10
EDDIE SAYS
Remember to multiply everything inside of the brackets by the multiplier which is outside the brackets. This will give us: 2 × x = 2x and 2 × 5 = 10 When we put these elements back together, we reach our answer: 2x + 10 Let's have a go at another question now.
• Question 2

Expand:

3(2x + 4)

6x + 12
6x+12
6x +12
6x+ 12
EDDIE SAYS
Did you follow the same method from Q1? 3 × 2x = 6x 3 × 4 = 12 When we put them back together, out answer is: 6x + 12
• Question 3

Expand:

7(3p - 2q)

21p - 14q
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 these elements back together and our answer is: 21p - 14q
• Question 4

Lisa and Ruby both expand: 4(3a - 5b)

Lisa says the answer is: 12a - 5b

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

Who is correct?

Ruby
EDDIE SAYS
It looks like Lisa forgot to multiply 4 and -5b! Ruby is correct, because she multiplied both terms in the bracket by the multiplier of 4. Her working may have looked something like this: 4 x 3a = 12a 4 x -5b = -20b Back together, they become: 12a - 20b -20b + 12a would also be correct as it means exactly the same thing.
• Question 5

Imagine that your friend's working is shown below.

The are trying to expand:

2(4y + 3)

Can you spot their mistake?

Underline where you think they first made a mistake.

2(4y + 3)

2 × 4y = 8y

2 × 3 = 5

2(4y + 3) = 8y + 5
EDDIE SAYS
In the third line of their working, your friend added 2 and 3 instead of multiplying them. An easy mistake to make! But this meant that their final answer was incorrect.
• Question 6

Imagine that your friend's working is shown below.

The are trying to expand:

-2(w - 5)

Can you spot their mistake?

Underline where you think they first made a mistake.

−2(w - 5)

−2 × 2 = −2w

−2 × −5 = −10

−2(w - 5) = −2w 10
EDDIE SAYS
Did you remember that a negative number multiplied by another negative gives a positive answer? This is why −2 × −5 = 10 Your friend wrote -10 rather than +10! So their answer should have been: −2(w - 5) = −2w + 10 That - rather than + symbol makes a big difference unfortunately!
• Question 7

True or false?

−5(3x + 1) = −15x + 1

False
EDDIE SAYS
Whoops! Somebody forgot to multiply the second element inside the brackets by the multiplier here. They should have calculated: -5 x 3x -5 x 1 Then put them back together to reach: -15x - 5 not -15x + 1
• Question 8

Find the expression for the area of the composite shape below. 6x + 12
6x+12
6x +12
6x+ 12
EDDIE SAYS
This is a sort of question you might get in an 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 rectangle? That's right, base × height. So the area of the bigger rectangle is 4(x + 3). If we expand these brackets, we reach 4x + 12. The area of the smaller rectangle is x × 2 = 2x Now we need to add these elements together and simplify: 4x + 12 + 2x = 6x + 12 That wasn't so difficult, was it?
• Question 9

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

What is the area of this rectangle?

EDDIE SAYS
To find area of a rectangle, we need to multiply its width by its length. In this case, its width is 6 and its length is (x + 7). So we need to calculate: 6(x + 7) 6 times x = 6x 6 times 7 = 42 If we put these together, we reach: 6x + 42 cm²
• Question 10

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

Write the correct numbers and / or mathematical symbols in the blanks in the expression below.

EDDIE SAYS
We find the area of a parallelogram in exactly the same way as the area of a rectangle: length × width. Our calculation needs to be: xy × (4yx - 1) = xy(4xy - 1) xy × 4xy = 4x²y² xy × −1 = −xy If put these elements back together, we reach: 4x²y² −xy Did you put a '4' in the first blank and a '-1' or just a '-' sign in the second? Great work completing this activity - hopefully expanding single brackets is now a doddle!
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