# Simple Factorising (3)

In this worksheet, students factorise algebraic expressions involving terms such as xy and x².

Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:

### 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 - 15x².

The HCF of 10x and 15x² is 5x.

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

The answer is 5x(2 - 3x)

(Check by multipling out the brackets again)

Factorise fully:

15x + 10xy

25xy

5x(3 + 2y)

5(3x + 2xy)

Factorise fully:

15x + 5xy

5x(3 + y)

5(3x + xy)

3 + y

Factorise fully:

15x - 25x2

5(3x - 5x)

5x(3 - 5x)

3x - 5x²

Factorise fully:

9x - 6yx

9(x - 6y)

3(3x - 2y)

3x(3 - 2y)

Factorise fully:

9x - 18x2

9x(1 - 2x)

3(3x - 6x²)

9x(   - 2x)

Factorise fully:

27y - 6xy

9(3x - 6y)

3y(9x - 6)

3y(9 - 2x)

Factorise fully:

8x - 6xy

2x(4 - 3y)

4(x - 6y)

4x(2 - 6y)

Factorise fully:

18x2 - 6x

6x(3x -   )

6x(3x - 0)

6x(3x - 1)

Factorise fully:

28xy + 21x

21x(7y + 0)

7xy(4 + 3)

7x(4y + 3)

Factorise fully:

28xy + 20x - 8x2

4x(7y + 5 - 2x)

7x(4 + 13x - x)

4(7xy + 5x - 2x²)

• Question 1

Factorise fully:

15x + 10xy

5x(3 + 2y)
EDDIE SAYS
The HCF of 15x + 10xy is 5x 5(3x + 2xy) is not FULLY factorised as 5 is not the HCF
• Question 2

Factorise fully:

15x + 5xy

5x(3 + y)
EDDIE SAYS
The HCF of 15x + 5xy is 5x 5(3x + xy) is not FULLY factorised as 5 is not the HCF
• Question 3

Factorise fully:

15x - 25x2

5x(3 - 5x)
EDDIE SAYS
The HCF of 15x - 25x2 is 5x
• Question 4

Factorise fully:

9x - 6yx

3x(3 - 2y)
EDDIE SAYS
The HCF of 9x - 6yx is 3x
• Question 5

Factorise fully:

9x - 18x2

9x(1 - 2x)
EDDIE SAYS
The HCF of 9x - 18x2 is 9x 3(3x - 6x²) is not fully factorised
• Question 6

Factorise fully:

27y - 6xy

3y(9 - 2x)
EDDIE SAYS
The HCF of 27y - 6xy is 3y
• Question 7

Factorise fully:

8x - 6xy

2x(4 - 3y)
EDDIE SAYS
The HCF of 8x - 6xy is 2x
• Question 8

Factorise fully:

18x2 - 6x

6x(3x - 1)
EDDIE SAYS
The HCF of 18x2 - 6x is 6x Remember that if you divide 6x by 6x you get 1 (not 0)
• Question 9

Factorise fully:

28xy + 21x

7x(4y + 3)
EDDIE SAYS
The HCF of 28xy + 21x is 7x
• Question 10

Factorise fully:

28xy + 20x - 8x2

4x(7y + 5 - 2x)
EDDIE SAYS
The HCF of 28xy + 20x - 8x2 is 4x
---- OR ----

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