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Pointers
Take out the common factor first, then factorise further using
the difference of two squares.a
2 b2= (a+ b)(a b)
Pointers
Expand 4(2p 7) using a(b c) = ab ac.
Expand (p 4)2using (a b)
2= a2 2ab+ b
2.
Simplify your answer.
CHAPTER 31: ALGEBRAIC EXPRESSIONS III
Cloned PMR Question (2006, Paper 2, Question 9)
Factorise completely 18 2m2.
Solution
18 2m2= 2(9 m
2)
= 2(3 + m)(3 m)
Cloned PMR Question (2006, Paper 2, Question 11)
Simplify 4(2p 7) + (p 4)2.
Solution
4(2p 7) + (p 4)2= 8p 28 + [p2 2(p)(4) + 42]
= 8p 28 +p2 8p + 16
=p2 12
NEXUS PMR MATHEMATICS FORM 1, 2 & 3
Page349 (More Cloned PMR Questions)Supplementary Materials
for
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Pointers
Perform subtraction of algebraic fractions using the lowest
common multiple (LCM).
The LCM of 4mand 12mvis 12mv.
Remember to simplify the single fraction obtained.
Cloned PMR Question (2006, Paper 2, Question 12)
Express
mv
v
m 12
4
4
1 as a single fraction in its simplest form.
Solution
mv
v
m 12
4
4
1 =
mv
v
vm
v
12
4
)3(4
)3(1
=mv
vv
12
)4(3
=mv
vv
12
43 +
=mv
v
12
44
=mv
v
12
)1(4
=mv
v
3
1
NEXUS PMR MATHEMATICS FORM 1, 2 & 3
Page349 (More Cloned PMR Questions)Supplementary Materials
for
Factorise the numerator and then
simplify the fraction.
1
3
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Pointers
For (a), take out the common factor. For (b), take out the
common factor first. Then, factorise further using the difference
of
two squares.
a2 b
2= (a + b)(a b)
Pointers For (a), expand using a(b+ c) = ab+ ac.
For (b), expand using (a b)2= a
2 2ab+ b
2.
Cloned PMR Question (2007, Paper 2, Question 7)
Factorise completely each of the following expressions:
(a) 3y+ 12(b) 20 5x2
Solution
(a) 3y+ 12 = 3(y+ 4)
(b) 20 5x2= 5(4 x
2)
= 5(2 +x)(2 x)
Cloned PMR Question (2007, Paper 2, Question 8)
Expand each of the following expressions:
(a)p(3 + r)(b) (5m n)2
Solution
(a)p(3 + r) = 3p+pr
(b) (5m n)2= (5m)
2 2(5m)(n) + (n)2
= 25m2 10mn+ n
2
NEXUS PMR MATHEMATICS FORM 1, 2 & 3
Page349 (More Cloned PMR Questions)Supplementary Materials
for
The common factor is 3.
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Pointers
Perform addition of algebraic fractions using the lowest common
multiple (LCM).
The LCM of 3nand 6nis 6n.
Then, simplify the single fraction obtained.
Cloned PMR Question (2007, Paper 2, Question 9)
Express
n
w
n 6
31
3
7 + as a single fraction in its simplest form.
Solution
n
w
n 6
31
3
7 + =
n
w
n 6
31
)2(3
)2(7 +
=n
w
6
3114 +
=n
w
6
315
=n
w
6
)5(3
=n
w
2
5
NEXUS PMR MATHEMATICS FORM 1, 2 & 3
Page349 (More Cloned PMR Questions)Supplementary Materials
for
Factorise the numerator and then
simplify the fraction.
1
2
