EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Special Products and Expansions
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
If
(
x
+
1
x
)
=
5
,
find the value of
(
x
2
+
1
x
2
)
(i)
24
(ii)
22
(iii)
26
(iv)
23
(v)
21
Question
2
2.
If
(
6
x
−
1
3
x
)
=
7
,
find the value of
(
36
x
2
+
1
9
x
2
)
(i)
50
(ii)
56
(iii)
52
(iv)
54
(v)
53
Question
3
3.
If
(
a
−
b
)
=
2
,
a
b
=
8
, find
(
a
2
−
b
2
)
(i)
9
(ii)
14
(iii)
11
(iv)
13
(v)
12
Question
4
4.
The value of
799
✕
799
is
(i)
638400
(ii)
638404
(iii)
638401
(iv)
638398
(v)
638402
Question
5
5.
Find the value of
55
3
+
60
3
−
115
3
(i)
1728000
(ii)
(-1331000)
(iii)
1331000
(iv)
(-1728000)
(v)
(-1138500)
Question
6
6.
Evaluate
(
j
2
−
1
)
(
j
4
+
j
2
+
1
)
=
(i)
j
6
+
2
j
4
−
1
(ii)
j
6
−
2
j
2
+
1
(iii)
j
6
+
2
j
4
+
2
j
2
+
1
(iv)
0
(v)
j
6
−
1
Question
7
7.
The value of
19
✕
16
is
(i)
301
(ii)
305
(iii)
304
(iv)
306
(v)
303
Question
8
8.
If
(
x
+
1
x
)
=
9
,
find the value of
(
x
3
+
1
x
3
)
(i)
702
(ii)
699
(iii)
703
(iv)
704
(v)
701
Question
9
9.
The value of
33
✕
33
is
(i)
1086
(ii)
1089
(iii)
1091
(iv)
1090
(v)
1088
Question
10
10.
If
(
a
+
b
+
c
)
=
12
,
(
a
2
+
b
2
+
c
2
)
=
72
, find
(
a
b
+
a
c
+
b
c
)
(i)
35
(ii)
39
(iii)
34
(iv)
37
(v)
36
Question
11
11.
If
(
a
+
b
)
=
8
,
a
b
=
12
, find
(
a
2
+
b
2
)
(i)
37
(ii)
42
(iii)
39
(iv)
41
(v)
40
Question
12
12.
(
3
2
a
+
3
b
)
2
(i)
(
9
4
a
2
+
6
a
b
+
9
b
2
)
(ii)
(
9
4
a
2
+
9
a
b
+
9
b
2
)
(iii)
(
13
6
a
2
+
9
a
b
+
9
b
2
)
(iv)
(
5
2
a
2
+
9
a
b
+
9
b
2
)
(v)
(
9
4
a
2
+
11
a
b
+
9
b
2
)
Question
13
13.
(
3
a
+
3
b
)
(
9
a
2
−
9
a
b
+
9
b
2
)
(i)
(
27
a
3
+
30
b
3
)
(ii)
(
26
a
3
+
27
b
3
)
(iii)
(
27
a
3
+
27
b
3
)
(iv)
(
28
a
3
+
27
b
3
)
(v)
(
27
a
3
+
24
b
3
)
Question
14
14.
Evaluate
(
j
1
3
+
k
1
3
)
(
j
2
3
−
j
1
3
k
1
3
+
k
2
3
)
=
(i)
j
+
k
(ii)
(
j
+
k
)
2
(iii)
j
−
k
(iv)
0
(v)
(
j
−
k
)
2
Question
15
15.
(
3
a
+
3
2
b
)
2
(i)
(
10
a
2
+
9
a
b
+
9
4
b
2
)
(ii)
(
8
a
2
+
9
a
b
+
9
4
b
2
)
(iii)
(
9
a
2
+
12
a
b
+
9
4
b
2
)
(iv)
(
9
a
2
+
9
a
b
+
9
4
b
2
)
(v)
(
9
a
2
+
6
a
b
+
9
4
b
2
)
Question
16
16.
Expand
(
x
−
1
x
)
2
(i)
x
2
−
2
+
1
x
3
(ii)
x
2
−
2
+
1
x
2
(iii)
4
x
2
−
2
+
1
x
2
(iv)
x
2
−
2
−
1
x
2
(v)
x
3
−
2
+
1
x
2
Question
17
17.
The value of
79
1
3
✕
79
1
3
is
(i)
6293
7
11
(ii)
6293
5
9
(iii)
6294
(iv)
6293
7
9
Question
18
18.
(
2
a
+
3
b
)
(
2
a
−
3
b
)
(i)
(
3
a
2
−
9
b
2
)
(ii)
(
4
a
2
−
7
b
2
)
(iii)
(
5
a
2
−
9
b
2
)
(iv)
(
4
a
2
−
9
b
2
)
(v)
(
4
a
2
−
12
b
2
)
Question
19
19.
(
−
2
a
+
2
b
)
2
(i)
(
4
a
2
−
6
a
b
+
4
b
2
)
(ii)
(
4
a
2
−
11
a
b
+
4
b
2
)
(iii)
(
4
a
2
−
8
a
b
+
4
b
2
)
(iv)
(
3
a
2
−
8
a
b
+
4
b
2
)
(v)
(
5
a
2
−
8
a
b
+
4
b
2
)
Question
20
20.
If
(
x
−
1
x
)
=
9
,
find the value of
(
x
2
+
1
x
2
)
(i)
85
(ii)
84
(iii)
82
(iv)
83
(v)
81
Question
21
21.
Expand
(
x
−
1
)
(
x
+
1
)
(
x
2
+
1
)
(i)
x
4
−
1
(ii)
−
2
x
3
−
2
x
(iii)
3
x
5
+
6
x
3
+
3
x
4
+
6
x
2
+
3
x
+
3
(iv)
x
5
+
x
4
+
x
3
+
x
2
Question
22
22.
(
a
+
b
)
2
(i)
(
a
2
+
5
a
b
+
b
2
)
(ii)
(
a
2
+
b
2
)
(iii)
(
2
a
b
+
b
2
)
(iv)
(
a
2
+
2
a
b
+
b
2
)
(v)
(
2
a
2
+
2
a
b
+
b
2
)
Question
23
23.
The value of
51
✕
54
is
(i)
2753
(ii)
2757
(iii)
2751
(iv)
2754
(v)
2755
Question
24
24.
Find
396
3
(i)
62099156
(ii)
62099126
(iii)
62099136
(iv)
62099116
(v)
62099146
Question
25
25.
If
h
1
3
+
i
1
3
+
j
1
3
= 0, then
(i)
(
h
+
i
+
j
)
=
3
h
i
j
(ii)
(
h
+
i
+
j
)
=
27
h
i
j
(iii)
(
h
+
i
+
j
)
=
3
h
1
3
i
1
3
j
1
3
(iv)
(
h
+
i
+
j
)
3
=
27
h
i
j
Assignment Key
1) (iv)
2) (v)
3) (v)
4) (iii)
5) (v)
6) (v)
7) (iii)
8) (i)
9) (ii)
10) (v)
11) (v)
12) (ii)
13) (iii)
14) (i)
15) (iv)
16) (ii)
17) (iv)
18) (iv)
19) (iii)
20) (iv)
21) (i)
22) (iv)
23) (iv)
24) (iii)
25) (iii)
