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Factorise Into a Single Bracket

In this worksheet, students will factorise into a single bracket by taking out algebraic factors.

'Factorise Into a Single Bracket' worksheet

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:  

Worksheet Overview

QUESTION 1 of 10

Sometimes the common factor that you need to find to be able to factorise an expression is not a number, but a letter.

Look for the highest power of each letter that will go into each of the terms of the expression. This will be your common factor to put outside the bracket.

 

Have a look at this example:

Factorise 3a3 + 2ab.

The common letter in both terms is a. The highest power of a that goes into both terms is 1, so the common factor is a. You need to put a outside of the bracket.

Put 3a2 + 2b inside of the bracket. This is because when you multiply a and 3a2 you get 3a3 and when you multiply a and 2b you get 2ab, which is the original expression.

The final answer is a(3a² + 2b).

Match the expressions to their factorised form.

Column A

Column B

p² + 9p
p²(2p + 9)
2p² - 9p
p(p + 9)
2p³ + 9p²
p²(2 - 9p)
2p² - 9p³
p(2p - 9)

True or false?

2x² + 5x = x(x + 5)

True

False

Jenny factorised an expression and got ab(4 + c) as her answer.

What was the question?

ab + 4abc

ab + 4c

4ab + abc

4ab - abc

Tick the expressions which have been factorised correctly.

6a² - 7a = a(6a - 7)

6a - 7a²b = a(6 - 7b)

6a² + 7ab = a(6a + 7b)

6a² + 7a²b = a²(6 + 7ab)

What is the correct factorised form of 4x³y + 5xy?

xy(4x + 5)

xy(4x² + 5)

x(4x²y + 5y)

y(4x³ + 5x)

Match the expressions to their correct factorised forms.

Column A

Column B

3y³ - 5xy²
y²(3y - 5x)
2y² + 3xy²
xy²(2xy + 3)
3xy³ - 5x²y
xy(3y² - 5x)
2x²y³ + 3xy²
y²(2 + 3x)

Factorise 5s³ - 7s²t².

s²(5s - 7t)

s²(5 - 7t²)

s²(5s - 7st²)

s²(5s - 7t²)

Tick the expressions which cannot be factorised.

2x² - xy

12x + 7y

x³ + 2y³

12xy + 5x²y

What is the perimeter of this rectangle?

xy + z

2xy + z

x(y + z)

2x(y + z)

Factorise 3x³y - 6x²y.

xy(3x² - 6x)

3x²y(x - 2)

x²y(3x - 6)

3x²y(x - 6)

  • Question 1

Match the expressions to their factorised form.

CORRECT ANSWER

Column A

Column B

p² + 9p
p(p + 9)
2p² - 9p
p(2p - 9)
2p³ + 9p²
p²(2p + 9)
2p² - 9p³
p²(2 - 9p)
EDDIE SAYS
Did you manage to find the common factors? The final two questions are the hardest. The common factor of 2p³ and 9p² is p² because it goes both into p³ and p². So p² goes outside of the bracket. Inside of the bracket you need 2p + 9 for one and 2 - 9p for the other question.
  • Question 2

True or false?

2x² + 5x = x(x + 5)

CORRECT ANSWER
False
EDDIE SAYS
This is not correct! Although the common factor outside of the bracket is correct, the bracket isn't right: it should read x(2x + 5). Well done if you managed to spot this!
  • Question 3

Jenny factorised an expression and got ab(4 + c) as her answer.

What was the question?

CORRECT ANSWER
4ab + abc
EDDIE SAYS
Option c is the correct one. ab is the common factor of 4ab and abc so it goes outside of the bracket. We are left with 4 + c to go into the bracket, giving ab(4 + c), the answer Jenny got!
  • Question 4

Tick the expressions which have been factorised correctly.

CORRECT ANSWER
6a² - 7a = a(6a - 7)
6a² + 7ab = a(6a + 7b)
6a² + 7a²b = a²(6 + 7ab)
EDDIE SAYS
There are three expressions which are correctly factorised. The second one is incorrect because in the bracket there should be (6 - 7a).
  • Question 5

What is the correct factorised form of 4x³y + 5xy?

CORRECT ANSWER
xy(4x² + 5)
EDDIE SAYS
xy(4x² + 5) is the correct option. The common factor of 4x³y and 5xy is xy. Inside of the bracket we need to get 4x² and 5.
  • Question 6

Match the expressions to their correct factorised forms.

CORRECT ANSWER

Column A

Column B

3y³ - 5xy²
y²(3y - 5x)
2y² + 3xy²
y²(2 + 3x)
3xy³ - 5x²y
xy(3y² - 5x)
2x²y³ + 3xy²
xy²(2xy + 3)
EDDIE SAYS
Remember to look for common factors first. Sometimes the common factor has a power higher than one, such as in 2y² + 3xy². Here the common factor is y².
  • Question 7

Factorise 5s³ - 7s²t².

CORRECT ANSWER
s²(5s - 7st²)
EDDIE SAYS
The common factor of 5s³ and 7s²t² is s², so it goes outside of the bracket. Inside the bracket you need 5s and 7st² (because s² × 5s is 5s³ and s² × 7st² is 7s²t²). The final answer is s²(5s - 7st²).
  • Question 8

Tick the expressions which cannot be factorised.

CORRECT ANSWER
12x + 7y
x³ + 2y³
EDDIE SAYS
12x + 7y cannot be factorised because 12x and 7y do not have a common factor. x³ + 2y³ cannot be factorised either, because x³ and 2y³ do not have any common factors.
  • Question 9

What is the perimeter of this rectangle?

CORRECT ANSWER
2x(y + z)
EDDIE SAYS
The perimeter means adding the lengths of all sides. xy + xz + xy + xz = 2xy + 2xz When we factorise, we get 2x(y + z).
  • Question 10

Factorise 3x³y - 6x²y.

CORRECT ANSWER
3x²y(x - 2)
EDDIE SAYS
This is a tricky question! Not only do 3x³y and 6x²y have a common algebraic factor (xsup2;y), they also have a common numerical factor (3). The correct answer is 3x²y(x - 2).
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