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Simple Factorising (2)

In this worksheet, students factorise simple algebraic expressions.

'Simple Factorising (2)' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Factorising is the reverse of multiplying out brackets.

We put an expression into brackets by taking out the highest common factor (HCF) of each term in the expression.

To work out what goes inside the brackets, we divide each term by this HCF.

 

Example

Factorise fully 10x - 15 + 25y

 

Answer

The HCF of 10x and 15 and 25y is 5.

So we take 5 outside the brackets and divide each term by 5 to work out what goes inside the brackets.

The answer is 5(2x - 3 + 5y)

 

Factorise fully:

15x + 100

115x

5(3x + 95)

5(3x + 20)

Factorise fully:

15x + 5y

5(3x + y)

5(3x + 5y)

3x + y

Factorise fully:

15x - 25y

5(3x + 5y)

5(3x - 5y)

3x - y

Factorise fully:

9x - 6y

9(x - 6y)

3(3x - 6y)

3(3x - 2y)

Factorise fully:

9x - 18y

9(x - 2y)

3(3x - 6y)

9(x - 2)

Factorise fully:

27x + 9y - 6

9(3x + y - 6)

3(9x + 3y - 6)

3(9x + 3y - 2)

Factorise fully:

8x - 4y - 6

2(4x - 2y - 3)

4(x - y - 6)

4(2x - y - 6)

Factorise fully:

18x + 12y - 6

6(3x + 2y -   )

6(3x + 2y - 0)

6(3x + 2y - 1)

Factorise fully:

28y - 14x + 21

21(7y - x + 0)

7y(4 - 2x + 3)

7(4y - 2x + 3)

Factorise fully:

28y + 20 - 24x

4(7y + 5 - 6x)

7y(4 + 13 - x)

7(4y + 13 - 6x)

  • Question 1

Factorise fully:

15x + 100

CORRECT ANSWER
5(3x + 20)
  • Question 2

Factorise fully:

15x + 5y

CORRECT ANSWER
5(3x + y)
  • Question 3

Factorise fully:

15x - 25y

CORRECT ANSWER
5(3x - 5y)
  • Question 4

Factorise fully:

9x - 6y

CORRECT ANSWER
3(3x - 2y)
  • Question 5

Factorise fully:

9x - 18y

CORRECT ANSWER
9(x - 2y)
EDDIE SAYS
3(3x-6y) is not FULLY factorised as 3 is not the HIGHEST common factor
  • Question 6

Factorise fully:

27x + 9y - 6

CORRECT ANSWER
3(9x + 3y - 2)
  • Question 7

Factorise fully:

8x - 4y - 6

CORRECT ANSWER
2(4x - 2y - 3)
  • Question 8

Factorise fully:

18x + 12y - 6

CORRECT ANSWER
6(3x + 2y - 1)
  • Question 9

Factorise fully:

28y - 14x + 21

CORRECT ANSWER
7(4y - 2x + 3)
  • Question 10

Factorise fully:

28y + 20 - 24x

CORRECT ANSWER
4(7y + 5 - 6x)
---- OR ----

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