year 8 maths

36 Chapter 1 Algebraic techniques 2 and indices
1H Factorising expressions
Factorising is the opposite procedure to expanding. It allows us to simplify
expressions and solve harder mathematical problems. Because 3(2x + 5)
expands to 6x + 15 , this means that the factorised form of 6x + 15 is 3(2x + 5) .
The aim when factorising is to write expressions as the product of two or more
factors.
Expanding
3(2x − 5) = 6x + 15
Factorising
Let’s start: Expanding gaps
• Try to fill in the gaps to make the following equivalence true: □ ( □ + □ ) = 12x + 18xy .
• In how many ways can this be done? Try to find as many ways as possible.
• If the aim is to make the term outside the brackets as large as possible, what is the best possible
solution to the puzzle?
Key ideas
■ The highest common factor (HCF) of a set of terms is the largest factor that divides into
each term. For example:
HCF of 15x and 21y is 3 .
HCF of 10a and 20c is 10 .
HCF of 12x and 18xy is 6x .
■To factorise an expression, first take the HCF of the terms outside the brackets and divide each
term by it, leaving the result in brackets.
For example:
10x + 15y
HCF = 5
Result 5(2x + 3y)
HCF 10x ÷ 5 15y ÷ 5
■ To check your answer, expand the factorised form.
For example: 5(2x + 3y) = 10x + 15y ✓
Example 14
Finding the highest common factor (HCF)
Find the highest common factor (HCF) of:
a 20 and 35 b 18a and 24ab c 12x and 15x 2
SOLUTION
EXPLANATION
a 5 5 is the largest number that divides into 20 and 35 .
b 6a
6 is the largest number that divides into 18 and 24 , and
a divides into both terms.
c 3x 3 divides into both 12 and 15 , and x divides into both terms.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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