year 8 maths

1G
Expanding brackets
35
16 Prove that 4a(2 + b) + 2ab is equivalent to a(6b + 4) + 4a by expanding both expressions.
17 Find an expanded expression for (x + y)(x + 2y) by considering the diagram below. Ensure your
answer is simplified by combining any like terms.
x
y
x
y
y
18 Prove that the following sequence of operations has the same effect as doubling a number.
1 Take a number, add 2 .
2 Multiply by 6 .
3 Subtract 6 .
1
4 Multiply this result by
3 .
5 Subtract 2 .
ENRICHMENT
– –
19
Expanding algebraic fractions
x + 5
19 To simplify + x 3 2
2(x + 5)
+ 3x
2x + 10
. Then expand to finish off the simplification:
6 6 6
Use this method to simplify the following sums.
x + 1
a + x 3 2
x + 5
b + x 5 3
3x
c
8 + x − 1
4
x + 2
d + x + 1
4 3
2x + 1
e + 3x + 1
5 10
f
2x − 1
7
+ 3x + 2
5
change both fractions to have a common denominator of 6 , giving
+ 3x
6
5x + 10
= .
6
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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