EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Special Products and Expansions
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
(
3
2
a
−
3
2
b
−
2
c
)
2
(i)
(
13
6
a
2
−
9
2
a
b
−
6
a
c
+
9
4
b
2
+
6
b
c
+
4
c
2
)
(ii)
(
9
4
a
2
−
11
2
a
b
−
6
a
c
+
9
4
b
2
+
6
b
c
+
4
c
2
)
(iii)
(
9
4
a
2
−
7
2
a
b
−
6
a
c
+
9
4
b
2
+
6
b
c
+
4
c
2
)
(iv)
(
5
2
a
2
−
9
2
a
b
−
6
a
c
+
9
4
b
2
+
6
b
c
+
4
c
2
)
(v)
(
9
4
a
2
−
9
2
a
b
−
6
a
c
+
9
4
b
2
+
6
b
c
+
4
c
2
)
Question
2
2.
The expanded form of
(
3
x
+
8
)
(
x
+
6
)
(
3
x
−
5
)
is
(i)
(
6
x
3
+
63
x
2
+
14
x
−
240
)
(ii)
(
10
x
3
+
63
x
2
+
14
x
−
240
)
(iii)
(
8
x
3
+
63
x
2
+
14
x
−
240
)
(iv)
(
11
x
3
+
63
x
2
+
14
x
−
240
)
(v)
(
9
x
3
+
63
x
2
+
14
x
−
240
)
Question
3
3.
(
2
a
−
3
2
b
)
2
(i)
(
4
a
2
−
4
a
b
+
9
4
b
2
)
(ii)
(
4
a
2
−
6
a
b
+
9
4
b
2
)
(iii)
(
3
a
2
−
6
a
b
+
9
4
b
2
)
(iv)
(
4
a
2
−
9
a
b
+
9
4
b
2
)
(v)
(
5
a
2
−
6
a
b
+
9
4
b
2
)
Question
4
4.
(
3
a
+
3
2
b
)
(
3
a
−
3
2
b
)
(i)
(
10
a
2
−
9
4
b
2
)
(ii)
(
9
a
2
−
9
4
b
2
)
(iii)
(
9
a
2
−
7
4
b
2
)
(iv)
(
8
a
2
−
9
4
b
2
)
(v)
(
9
a
2
−
11
4
b
2
)
Question
5
5.
If
(
a
2
+
b
2
)
=
34
,
a
b
=
15
, find
(
a
+
b
)
(i)
9
(ii)
10
(iii)
7
(iv)
6
(v)
8
Question
6
6.
Expand
(
x
+
1
x
)
2
(i)
4
x
2
+
2
+
1
x
2
(ii)
x
2
+
1
+
1
x
2
(iii)
x
2
+
2
+
1
x
2
(iv)
−
2
x
2
+
2
+
1
x
2
(v)
x
2
+
3
+
1
x
2
Question
7
7.
If
(
a
+
b
+
c
)
=
22
,
(
a
2
+
b
2
+
c
2
)
=
164
, find
(
a
b
+
a
c
+
b
c
)
(i)
159
(ii)
163
(iii)
161
(iv)
158
(v)
160
Question
8
8.
The value of
41
✕
41
is
(i)
1684
(ii)
1682
(iii)
1678
(iv)
1680
(v)
1681
Question
9
9.
(
−
2
a
+
3
b
)
(
−
2
a
−
3
b
)
(i)
(
3
a
2
−
9
b
2
)
(ii)
(
4
a
2
−
9
b
2
)
(iii)
(
4
a
2
−
12
b
2
)
(iv)
(
4
a
2
−
6
b
2
)
(v)
(
5
a
2
−
9
b
2
)
Question
10
10.
The value of
31
✕
29
is
(i)
899
(ii)
896
(iii)
900
(iv)
901
(v)
898
Question
11
11.
If
(
x
+
1
x
)
=
6
,
find the value of
(
x
4
+
1
x
4
)
(i)
1153
(ii)
1151
(iii)
1155
(iv)
1154
(v)
1156
Question
12
12.
(
−
2
a
+
3
b
)
3
(i)
(
−
7
a
3
+
36
a
2
b
−
54
a
b
2
+
27
b
3
)
(ii)
(
−
8
a
3
+
33
a
2
b
−
54
a
b
2
+
27
b
3
)
(iii)
(
−
8
a
3
+
36
a
2
b
−
54
a
b
2
+
27
b
3
)
(iv)
(
−
8
a
3
+
38
a
2
b
−
54
a
b
2
+
27
b
3
)
(v)
(
−
9
a
3
+
36
a
2
b
−
54
a
b
2
+
27
b
3
)
Question
13
13.
Find the value of
3
3
+
6.6
3
−
9.6
3
(i)
-570.24
(ii)
2299.968
(iii)
216
(iv)
-216
(v)
-2299.968
Question
14
14.
Expand
(
x
−
1
x
)
2
(i)
x
2
−
2
−
1
x
2
(ii)
x
2
−
2
+
1
x
3
(iii)
x
2
−
1
+
1
x
2
(iv)
x
2
−
2
+
1
x
2
(v)
x
2
+
0
+
1
x
2
Question
15
15.
If
(
49
a
2
+
9
b
2
)
=
1261
,
a
b
=
10
, find
(
7
a
+
3
b
)
(i)
42
(ii)
43
(iii)
41
(iv)
40
(v)
38
Question
16
16.
(
a
+
b
)
(
a
−
b
)
(i)
(
a
2
−
b
2
)
(ii)
(
2
a
2
−
b
2
)
(iii)
(
−
b
2
)
(iv)
(
a
2
+
2
b
2
)
(v)
(
a
2
−
4
b
2
)
Question
17
17.
Evaluate
(
b
2
−
1
)
(
b
4
+
b
2
+
1
)
=
(i)
0
(ii)
b
6
−
1
(iii)
b
6
+
2
b
4
−
1
(iv)
b
6
−
2
b
2
+
1
(v)
b
6
+
2
b
4
+
2
b
2
+
1
Question
18
18.
Find the value of
15
3
+
25
3
−
40
3
(i)
(-27000)
(ii)
(-45000)
(iii)
27000
(iv)
125000
(v)
(-125000)
Question
19
19.
If
(
x
−
1
x
)
=
5
,
find the value of
(
x
4
+
1
x
4
)
(i)
725
(ii)
728
(iii)
727
(iv)
726
(v)
729
Question
20
20.
(
a
+
b
+
c
)
2
(i)
(
a
2
+
4
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(ii)
(
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iii)
(
2
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iv)
(
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(v)
(
a
2
−
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
Question
21
21.
Expand
(
x
−
1
)
(
x
+
1
)
(
x
2
+
1
)
(i)
x
4
−
1
(ii)
x
5
+
x
4
+
x
3
+
x
2
(iii)
3
x
5
+
6
x
3
+
3
x
4
+
6
x
2
+
3
x
+
3
(iv)
−
2
x
3
−
2
x
Question
22
22.
If
(
x
2
+
1
x
2
)
=
27
,
find the value of
(
x
−
1
x
)
(i)
2
(ii)
5
(iii)
4
(iv)
8
(v)
6
Question
23
23.
If
(
a
2
−
b
2
)
=
12
,
a
b
=
8
, find
(
a
−
b
)
(i)
5
(ii)
3
(iii)
0
(iv)
1
(v)
2
Question
24
24.
(
a
−
b
)
2
(i)
(
a
2
−
5
a
b
+
b
2
)
(ii)
(
−
2
a
b
+
b
2
)
(iii)
(
a
2
+
b
2
)
(iv)
(
2
a
2
−
2
a
b
+
b
2
)
(v)
(
a
2
−
2
a
b
+
b
2
)
Question
25
25.
Evaluate
(
c
1
3
+
d
1
3
)
(
c
2
3
−
c
1
3
d
1
3
+
d
2
3
)
=
(i)
(
c
−
d
)
2
(ii)
c
−
d
(iii)
0
(iv)
c
+
d
(v)
(
c
+
d
)
2
Assignment Key
1) (v)
2) (v)
3) (ii)
4) (ii)
5) (v)
6) (iii)
7) (v)
8) (v)
9) (ii)
10) (i)
11) (iv)
12) (iii)
13) (i)
14) (iv)
15) (iii)
16) (i)
17) (ii)
18) (ii)
19) (iii)
20) (iv)
21) (i)
22) (ii)
23) (v)
24) (v)
25) (iv)
