Algebraic Manipulations Worksheet With Answer Key Page 4
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1
2
3
4
5
6
71 − 58
−
2
2
−
2
68. Factorise completely
24 6a
5
a
b
2
a
= , find the value of
4
80. Given that
3
b
b
69. Express as a single fraction in its simplest form
p
2
−
−
+
−
2
2
81. Factorise completely
x
2
xy y
9
+
−
3
p
1
p
3
4
1
−
+
+
− +
−
70. Factorise completely 5
m
12(
m
1)(
m
1) 9
82. Express
as a fraction in its simplest
−
−
2
x
3
x
9
form
−
5
a
2
a
9
−
71. Simplify
−
−
2
2
a
9 9
a
−
+
−
2
83. Factorise completely
6
x
19
x
10
2
+
2
=
ab = , calculate the
72. Given that
a
b
17
and
3
2
3
−
84. Express
as a single fraction in its
−
−
−
2
2
−
+
value of
(2
a
2 )
b
(
a b
)
x
2
x
3
lowest terms.
−
−
+
73. (a) Factorise completely 4
ac
3
bc
4
ad
3
bd
− −
2
3
x
2
x
a
≠ , find the value of
(b) Given that c d
when
85. Simplify
b
−
x
2
−
−
+
=
4
ac
3
bc
4
ad
3
bd
0
3
2
x
−
−
2
−
−
2
+
2
74. Express
as a single fraction in
86. Factorise completely
(3
x y
)
3(
x y
)
2
x
−
−
+
2
x
3
x
7
x
12
its simplest form
−
+ = , express y interms
2 2
87. Given that
4
x y
12
xy
9
k
−
5
2
x
3
−
k > .
75. Express
as a fraction in its lowest
of x and k, where
0
−
2
− −
x
3
x
x
6
terms.
3
2
−
88. Simplify
−
−
2
y
8 3
y
12
2
+
+
76. (a) Factorise
3
a
10
a
7
(b) Hence, find 2 factors of 31007 other than 1 and
+
−
−
31007.
89. Factorise completely 15
ax
21
bx
14
by
10
ay
+
= − and
−
=
(
)
77. Given that
x
2
y
2
x
2
y
18
, find the
−
1
−
−
5
1
2
2p qr
value of
90. Simplify the expression
, leaving your
( )
−
1
−
0
1
−
2
2
2
p
q r
(a)
x
4
y
answer in positive index form.
+
2
2
(b)
x
4
y
−
9
t
3
t
1
+
4
1
91. Express
as a single fraction in its
−
78. Simplify
2
−
−
2
9
t
4 2
t
3
t
−
−
2
2
12
x
3 6
x
3
x
simplest form
−
+
2
x
2
x
1
92. Make x the subject of the formula
−
79. Simplify
−
−
2
x
1
1
x
−
x y
= +
−
a b c
2
+
x y
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