year 8 maths

1G
Expanding brackets
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1G Expanding brackets
Two expressions might look quite different when in fact they are equivalent. For example, 2(3 − 7b) is
equivalent to 4b + 6(1 − 3b) even though they look quite different. One use for expanding brackets is
that it allows us quite easily to convert between equivalent expressions.
Let’s start: Room plans
An architect has prepared floor plans for a house but some numbers are missing. Four students have
attempted to describe the total area of the plans shown.
a 10
Alice says it is 5a + 50 + ab .
Brendan says it is 5(a + 10) + ab .
5
Charles says it is a(5 + b) + 50 .
David says it is (5 + b)(a + 10) − 10b .
• Discuss which of the students is correct.
b
• How do you think each student worked out their answer?
• The architect later told them that a = 4 and b = 2 . What value
would each of the four students get for the area?
Key ideas
■ The distributive law is used to rewrite an expression without the brackets.
• a(b + c) = a × b + a × c
= ab + ac
• a(b − c) = a × b − a × c
= ab − ac
For example: 4(2x + 5) = 8x + 20 and 3(5 − 2y) = 15 − 6y .
■ The distributive law can be illustrated by considering rectangle areas.
b
c
a a × b a × c
Area = a(b + c)
Area = ab + ac
■ The distributive law is used in arithmetic. For example:
5 × 31 = 5 × (30 + 1)
= 5 × 30 + 5 × 1
= 150 + 5
= 155
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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