year 8 maths

1H
Factorising expressions
39
13 Consider the diagram shown below. What is the factorised form of xy + 3x + 2y + 6 ?
y 3
x xy 3x
2
2y
6
14 In English, people often convert between ‘factorised’ and ‘expanded’ sentences. For instance,
‘I like John and Mary’ is equivalent in meaning to ‘I like John and I like Mary’. The first form is
factorised with the common factor that I like them. The second form is expanded.
a Expand the following sentences.
i I eat fruit and vegetables.
ii Rohan likes Maths and English.
iii Petra has a computer and a television.
iv Hayden and Anthony play tennis and chess.
b Factorise the following sentences.
i I like sewing and I like cooking.
ii Olivia likes ice-cream and Mary likes ice-cream.
iii Brodrick eats chocolate and Brodrick eats fruit.
iv Adrien likes chocolate and Adrien likes soft drinks, and Ben likes chocolate and Ben likes
soft drinks.
ENRICHMENT
– –
15
Factorising fractions
5x + 10
15 Factorising can be used to simplify algebraic fractions. For example, can be simplified by
7x + 14
5(x + 2)
first factorising the numerator and the denominator
7(x + 2) = 5 . Factorise and then simplify the
7
following fractions as much as possible.
a
d
g
2x + 4
5x + 10
4a + 2b
8c + 10d
7a − 21
2a − 6
b
e
h
7x − 7
2x − 2
5q − 15
3q − 9
12p
8p + 2pq
c
f
i
3ac + 5a
a + 2ab
7p + 14pq
9p + 18pq
100 − 10x
20 − 2x
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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