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Factorise Into a Single Bracket

In this worksheet, students will factorise expressions with numeric factors.

'Factorise Into a Single Bracket' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Factorising is the opposite of expanding brackets.

To factorise an expression, you need to look for a common factor. It might be a number, or might be a letter. Today we are going to look at expressions where a common factor is a number.

 

Here's a typical question on this topic:

Factorise 12x - 18y.

 

Look at the numbers. We need to find the highest common factor of 12 and 18.

The factors of 12 are 1, 2, 3, 4, 6, 12.

The factors of 18 are 1, 2, 3, 6, 9, 18.

The highest factor which they have in common is 6, so 6 goes outside of the bracket.

6( __   __ )

 

Now we need to work out the inside of the bracket.

 

6 × 2x = 12x, so we need to put 2x in the bracket

6 × -3y = -18y, so we need to put -3y in the bracket

 

The final answer is 12x - 18y = 6(2x - 3y).

Tick the highest common factor of 24 and 18.

1

2

4

6

Match the expressions to their correct factorised form.

Column A

Column B

5a + 15b
5(a + 3b)
25a - 5b
5(3a - 4b)
15a - 10b
5(4a - b)
15a - 20b
5(3a - 2b)
20a - 5b
5(5a - b)

Factorise 4a - 12b

Is it possible to factorise 8y + 3x?

Yes

No

Cannot tell

Alex and Rose are trying to factorise 14x + 28.

Alex says that the correct factorisation is 7(2x + 4).

Rose says that the correct answer is 2(2x + 14).

Who is right?

Rose

Alex

Neither of them as both are wrong

Fill in the blanks to factorise 8a + 12b - 4c completely.

Rose

Alex

Neither of them as both are wrong

Rory has factorised an expression and his answer is 3(3 − 7b).

What was the expression that he factorised? 

3 - 7b

33 - 37b

21b - 9

9 - 21b

Factorise the following fully

 

6x + 21

3(x + 21)

3(2x + 7)

3(x + 7)

3(2x + 21)

Which expression is equivalent to 3(2a + 8b)?

6a + 8b

6(a + 8b)

6a + 11b

6(a + 4b)

Factorise fully 10x2 - 5

Answer: 5(2x2 _____)

What should be written in the highlighted space above?

0

+ 1

- 1

+ 2

  • Question 1

Tick the highest common factor of 24 and 18.

CORRECT ANSWER
6
EDDIE SAYS
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 18 are 1, 2, 3, 6, 9, 18. The highest common factor of 24 and 18 is 6.
  • Question 2

Match the expressions to their correct factorised form.

CORRECT ANSWER

Column A

Column B

5a + 15b
5(a + 3b)
25a - 5b
5(5a - b)
15a - 10b
5(3a - 2b)
15a - 20b
5(3a - 4b)
20a - 5b
5(4a - b)
EDDIE SAYS
This is a little tricky as for every expression the highest common factor is 5. The best way to approach this question is to carefully factorise each expression. Let's have a look at a couple of those together. In 5a + 15b the common factor is 5, which goes outside of the bracket. What would go inside? 5 x a = 5a and 5 x 3b = 15b, so we'll have a and 3b inside of the bracket. So 5a + 15b = 5(a + 3) This question can be done in the same way: 25a - 5b. 5 x 5a = 25a 5 x -b = -5b So the factorised bracket will be 5(5a - b).
  • Question 3

Factorise 4a - 12b

CORRECT ANSWER
4(a-3b)
4(a -3b)
4(a - 3b)
EDDIE SAYS
The common factor of 4 and 12 is 4, so 4 goes outside of the bracket. 4 × a = 4a 4 × -3b = -12 So the answer is 4(a -3b).
  • Question 4

Is it possible to factorise 8y + 3x?

CORRECT ANSWER
No
EDDIE SAYS
8y + 3x cannot be factorised because 8 and 3 do not have a common factor other than 1.
  • Question 5

Alex and Rose are trying to factorise 14x + 28.

Alex says that the correct factorisation is 7(2x + 4).

Rose says that the correct answer is 2(2x + 14).

Who is right?

CORRECT ANSWER
Neither of them as both are wrong
EDDIE SAYS
Both girls are wrong here because neither of them used the HIGHEST common factor of 14 and 28 for their factorisation. Let's look at factors of 14 and 28. 14: 1, 2, 7, 14 28: 1, 2, 4, 5, 14, 28 The highest common factor is 14, so the correct answer is 14(x + 2)
  • Question 6

Fill in the blanks to factorise 8a + 12b - 4c completely.

CORRECT ANSWER
EDDIE SAYS
There are three terms in this expression, 8a, 12 b and 4c, but we can still factorise it by finding the highest common factor on 8, 12 and 4. The highest common factor of these three is 4, so we put it outside of the bracket and then work out what needs to go inside of the bracket. We will have three terms in the brackets rather than two, but it's ok! The answer should be 8a + 12b - 4c = 4(2a + 3b - c)
  • Question 7

Rory has factorised an expression and his answer is 3(3 − 7b).

What was the expression that he factorised? 

CORRECT ANSWER
9 - 21b
EDDIE SAYS
To check what expression has been factorised, we need to do the opposite, which is expanding brackets. When we expand 3(3 - 7b) we get 9 - 21b, so this is the expression that Rory factorised.
  • Question 8

Factorise the following fully

 

6x + 21

CORRECT ANSWER
3(2x + 7)
EDDIE SAYS
The highest common factor of 6 and 21 is 3. 3 goes outside of the bracket. 3 × 2x = 6x 3 × 7= 21 6x and 21 go inside of the bracket. The final answer when we put these together is 3(2x + 7).
  • Question 9

Which expression is equivalent to 3(2a + 8b)?

CORRECT ANSWER
6(a + 4b)
EDDIE SAYS
Did you try expanding the brackets and then factorising again? 3(2a + 8b) = 6a + 24b, so neither of the expanded forms in the answers are correct. The highest common factor of 6 and 24 is 6. 6 × a = 6a 6 × 4b = 24b Just put these together to reveal the correct answer 6(a + 4b).
  • Question 10

Factorise fully 10x2 - 5

Answer: 5(2x2 _____)

What should be written in the highlighted space above?

CORRECT ANSWER
- 1
EDDIE SAYS
The answer is -1 because to get -5 we need to multiply 5 (the common factor) by -1.
---- OR ----

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