year 8 maths

1G
Expanding brackets
33
3 Consider this combined rectangle, which has an area of 6(a + 7) .
a What is the area of the purple rectangle?
b What is the area of the orange rectangle?
c Write an expression for the sum of these two areas.
d Write the expanded form for 6(a + 7) .
6
a
7
4 Which of the following is the correct expansion of 4(3x + 7) ?
A 12x + 7 B 4x + 28 C 3x + 28 D 12x + 28
5 Complete the following expansions.
a 2(b + 5) = 2b + □
b 3(2x + 4y) = 6x + □ y
c 5(3a − 2) = 15a − □
d 7(4x − 2y) = 28x − □ y
Example 12a,b
Example 12c
Example 13
6 Use the distributive law to expand these expressions.
a 9(a + 7) b 2(2 + t) c 8(m − 10) d 3(8 − v)
e −5(9 + g) f −7(5b + 4) g −9(u + 9) h −8(5 + h)
i 5(6 − j) j 6(2 − m) k 3(10 − b) l 2(c − 8)
7 Use the distributive law to remove the grouping symbols.
a 8z(k − h) b 6j(k + a) c 4u(r − 2q) d 2p(3c − v)
e m(10a + v) f −2s(s + 5g) g −3g(8q + g) h −f(n + 4f )
i −8u(u + 10t) j −s(t + 5s) k m(2h − 9m) l 4a(5w − 10a)
8 S i mplify the following by expanding and then collecting like terms.
a 7(9f + 10) + 2f
b 8(2 + 5x) + 4x
c 4(2a + 8) + 7a
d 6(3v + 10) + 6v
e 7(10a + 10) + 6a
f 6(3q − 5) + 2q
g 6(4m − 5) + 8m
h 4(8 + 7m) − 6m
9 The distributive law also allows expansion with more than two terms in the brackets, for instance
3(2x − 4y + 5) = 6x − 12y + 15 . Use this fact to simplify the following.
a 2(3x + 2y + 4z) b 7a(2 − 3b + 4y)
c 2q(4z + 2a + 5) d −3(2 + 4k + 2p)
e −5(1 + 5q − 2r) f −7k(r + m + s)
10 Simplify the following by expanding and then collecting like terms.
a 3(3 + 5d) + 4(10d + 7)
b 10(4 + 8f ) + 7(5f + 2)
c 2(9 + 10j) + 4(3j + 3)
d 2(9 + 6d ) + 7(2 + 9d )
e 6(10 − 6j) + 4(10j − 5)
f 8(5 + 10g) + 3(4 − 4g)
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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