EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Special Products and Expansions
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
If
(
a
+
b
+
c
)
=
20
,
(
a
2
+
b
2
+
c
2
)
=
138
, find
(
a
b
+
a
c
+
b
c
)
(i)
128
(ii)
132
(iii)
131
(iv)
130
(v)
133
Question
2
2.
(
a
+
b
+
c
)
(
a
2
−
a
b
−
a
c
+
b
2
−
b
c
+
c
2
)
(i)
(
−
3
a
b
c
+
b
3
+
c
3
)
(ii)
(
a
3
−
3
a
b
c
+
b
3
+
c
3
)
(iii)
(
a
3
+
b
3
+
c
3
)
(iv)
(
2
a
3
−
3
a
b
c
+
b
3
+
c
3
)
(v)
(
a
3
−
6
a
b
c
+
b
3
+
c
3
)
Question
3
3.
If
(
x
4
+
1
x
4
)
=
2599
,
find the value of
(
x
−
1
x
)
(i)
7
(ii)
6
(iii)
9
(iv)
8
(v)
4
Question
4
4.
If
(
x
−
1
x
)
=
9
,
find the value of
(
x
3
−
1
x
3
)
(i)
757
(ii)
758
(iii)
756
(iv)
753
(v)
755
Question
5
5.
Expand
(
x
+
1
x
)
2
(i)
x
2
+
2
+
1
x
2
(ii)
x
+
2
+
1
x
2
(iii)
x
2
+
2
+
4
x
2
(iv)
−
x
2
+
2
+
1
x
2
(v)
x
2
+
2
+
1
x
Question
6
6.
(
3
2
a
−
3
2
b
)
2
(i)
(
9
4
a
2
−
11
2
a
b
+
9
4
b
2
)
(ii)
(
5
2
a
2
−
9
2
a
b
+
9
4
b
2
)
(iii)
(
9
4
a
2
−
9
2
a
b
+
9
4
b
2
)
(iv)
(
13
6
a
2
−
9
2
a
b
+
9
4
b
2
)
(v)
(
9
4
a
2
−
7
2
a
b
+
9
4
b
2
)
Question
7
7.
If
(
a
+
b
)
=
11
,
a
b
=
30
, find
(
a
3
+
b
3
)
(i)
339
(ii)
342
(iii)
341
(iv)
340
(v)
344
Question
8
8.
If
(
x
2
+
1
x
2
)
=
83
,
find the value of
(
x
−
1
x
)
(i)
10
(ii)
6
(iii)
8
(iv)
11
(v)
9
Question
9
9.
Evaluate
(
a
1
2
+
b
1
2
)
(
a
1
2
−
b
1
2
)
=
(i)
(
a
+
b
)
(ii)
1
(iii)
0
(iv)
(
a
+
b
)
2
(v)
(
a
−
b
)
Question
10
10.
If
(
a
2
+
b
2
)
=
61
,
a
b
=
30
, find
(
a
+
b
)
(i)
8
(ii)
11
(iii)
12
(iv)
14
(v)
10
Question
11
11.
If
(
2
a
+
3
b
)
=
21
,
a
b
=
18
, find
(
16
a
4
+
81
b
4
)
(i)
27298
(ii)
27295
(iii)
27297
(iv)
27300
(v)
27296
Question
12
12.
If
(
x
2
+
1
x
2
)
=
47
,
find the value of
(
x
+
1
x
)
(i)
8
(ii)
6
(iii)
10
(iv)
4
(v)
7
Question
13
13.
Find the value of
1.4
3
+
7.6
3
−
9
3
(i)
21.952
(ii)
-21.952
(iii)
3511.808
(iv)
-3511.808
(v)
-287.28
Question
14
14.
If
(
5
x
−
1
3
x
)
=
3
,
find the value of
(
25
x
2
+
1
9
x
2
)
(i)
13
(ii)
37
3
(iii)
61
5
(iv)
35
3
Question
15
15.
(
−
4
a
−
3
b
)
2
(i)
(
17
a
2
+
24
a
b
+
9
b
2
)
(ii)
(
16
a
2
+
24
a
b
+
9
b
2
)
(iii)
(
16
a
2
+
27
a
b
+
9
b
2
)
(iv)
(
16
a
2
+
22
a
b
+
9
b
2
)
(v)
(
15
a
2
+
24
a
b
+
9
b
2
)
Question
16
16.
(
a
−
b
)
3
(i)
(
−
3
a
2
b
+
3
a
b
2
−
b
3
)
(ii)
(
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
)
(iii)
(
2
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
)
(iv)
(
a
3
−
5
a
2
b
+
3
a
b
2
−
b
3
)
(v)
(
a
3
−
a
2
b
+
3
a
b
2
−
b
3
)
Question
17
17.
(
a
+
5
b
)
3
(i)
(
2
a
3
+
15
a
2
b
+
75
a
b
2
+
125
b
3
)
(ii)
(
a
3
+
12
a
2
b
+
75
a
b
2
+
125
b
3
)
(iii)
(
a
3
+
17
a
2
b
+
75
a
b
2
+
125
b
3
)
(iv)
(
15
a
2
b
+
75
a
b
2
+
125
b
3
)
(v)
(
a
3
+
15
a
2
b
+
75
a
b
2
+
125
b
3
)
Question
18
18.
The value of
500
3
4
✕
500
1
4
is
(i)
250500
5
16
(ii)
250500
3
16
(iii)
250500
1
16
(iv)
250500
3
14
(v)
250500
1
6
Question
19
19.
Find the value of
15
3
+
45
3
−
60
3
(i)
27000
(ii)
(-121500)
(iii)
(-27000)
(iv)
(-729000)
(v)
729000
Question
20
20.
The value of
36
✕
32
is
(i)
1152
(ii)
1155
(iii)
1149
(iv)
1151
(v)
1153
Question
21
21.
(
3
2
a
−
3
b
)
3
(i)
(
27
8
a
3
−
83
4
a
2
b
+
81
2
a
b
2
−
27
b
3
)
(ii)
(
27
8
a
3
−
81
4
a
2
b
+
81
2
a
b
2
−
27
b
3
)
(iii)
(
33
10
a
3
−
81
4
a
2
b
+
81
2
a
b
2
−
27
b
3
)
(iv)
(
27
8
a
3
−
79
4
a
2
b
+
81
2
a
b
2
−
27
b
3
)
(v)
(
7
2
a
3
−
81
4
a
2
b
+
81
2
a
b
2
−
27
b
3
)
Question
22
22.
If
(
a
+
b
+
c
)
=
13
,
(
a
b
+
a
c
+
b
c
)
=
56
, find
(
a
2
+
b
2
+
c
2
)
(i)
60
(ii)
57
(iii)
54
(iv)
56
(v)
58
Question
23
23.
If
(
a
−
b
)
=
1
,
a
b
=
6
, find
(
a
2
−
b
2
)
(i)
5
(ii)
7
(iii)
2
(iv)
6
(v)
4
Question
24
24.
Evaluate
(
g
2
−
1
)
(
g
4
+
g
2
+
1
)
=
(i)
0
(ii)
g
6
+
2
g
4
−
1
(iii)
g
6
−
2
g
2
+
1
(iv)
g
6
+
2
g
4
+
2
g
2
+
1
(v)
g
6
−
1
Question
25
25.
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
(i)
(
a
3
+
3
b
3
)
(ii)
b
3
(iii)
(
2
a
3
+
b
3
)
(iv)
(
a
3
−
2
b
3
)
(v)
(
a
3
+
b
3
)
Assignment Key
1) (iii)
2) (ii)
3) (i)
4) (iii)
5) (i)
6) (iii)
7) (iii)
8) (v)
9) (v)
10) (ii)
11) (iii)
12) (v)
13) (v)
14) (ii)
15) (ii)
16) (ii)
17) (v)
18) (ii)
19) (ii)
20) (i)
21) (ii)
22) (ii)
23) (i)
24) (v)
25) (v)
