EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Special Products and Expansions
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Evaluate
(
d
1
2
+
e
1
2
)
(
d
1
2
−
e
1
2
)
=
(i)
(
d
−
e
)
(ii)
(
d
+
e
)
(iii)
0
(iv)
1
(v)
(
d
+
e
)
2
Question
2
2.
(
−
2
3
a
+
2
b
+
3
c
)
(
4
9
a
2
+
4
3
a
b
+
2
a
c
+
4
b
2
−
6
b
c
+
9
c
2
)
(i)
(
−
8
27
a
3
+
12
a
b
c
+
8
b
3
+
27
c
3
)
(ii)
(
−
8
25
a
3
+
12
a
b
c
+
8
b
3
+
27
c
3
)
(iii)
(
−
8
29
a
3
+
12
a
b
c
+
8
b
3
+
27
c
3
)
(iv)
(
−
8
27
a
3
+
14
a
b
c
+
8
b
3
+
27
c
3
)
(v)
(
−
8
27
a
3
+
10
a
b
c
+
8
b
3
+
27
c
3
)
Question
3
3.
If
c
1
3
+
d
1
3
+
e
1
3
= 0, then
(i)
(
c
+
d
+
e
)
=
3
c
d
e
(ii)
(
c
+
d
+
e
)
=
3
c
1
3
d
1
3
e
1
3
(iii)
(
c
+
d
+
e
)
3
=
27
c
d
e
(iv)
(
c
+
d
+
e
)
=
27
c
d
e
Question
4
4.
The expanded form of
(
x
+
7
)
(
x
−
6
)
(
x
+
9
)
(
x
+
6
)
is
(i)
(
2
x
4
+
16
x
3
+
27
x
2
−
576
x
−
2268
)
(ii)
(
x
4
+
16
x
3
+
27
x
2
−
576
x
−
2268
)
(iii)
(
16
x
3
+
27
x
2
−
576
x
−
2268
)
(iv)
(
4
x
4
+
16
x
3
+
27
x
2
−
576
x
−
2268
)
(v)
(
−
x
4
+
16
x
3
+
27
x
2
−
576
x
−
2268
)
Question
5
5.
If
(
x
−
1
x
)
=
7
,
find the value of
(
x
2
+
1
x
2
)
(i)
53
(ii)
51
(iii)
48
(iv)
52
(v)
50
Question
6
6.
If
(
4
a
+
3
b
)
=
32
,
a
b
=
20
, find
(
256
a
4
+
81
b
4
)
(i)
180737
(ii)
180736
(iii)
180734
(iv)
180739
(v)
180735
Question
7
7.
The value of
199
2
3
✕
199
2
3
is
(i)
39866
5
9
(ii)
39866
7
11
(iii)
39867
(iv)
39866
7
9
Question
8
8.
If
(
2
a
+
2
b
)
=
10
,
a
b
=
6
, find
(
8
a
3
+
8
b
3
)
(i)
280
(ii)
279
(iii)
283
(iv)
281
(v)
277
Question
9
9.
(
−
a
+
b
)
(
a
2
+
a
b
+
b
2
)
(i)
(
−
2
a
3
+
b
3
)
(ii)
(
−
a
3
+
b
3
)
(iii)
b
3
(iv)
(
−
a
3
+
4
b
3
)
(v)
(
−
a
3
−
b
3
)
Question
10
10.
(
k
1
3
+
l
1
3
+
m
1
3
)
(
k
2
3
+
l
2
3
+
m
2
3
−
k
1
3
l
1
3
−
l
1
3
m
1
3
−
m
1
3
k
1
3
)
=
(i)
(
k
−
l
−
m
)
(ii)
k
+
l
+
m
−
3
m
1
3
k
1
3
l
1
3
(iii)
0
(iv)
(
k
+
l
+
m
)
2
(v)
(
k
−
l
−
m
)
2
Question
11
11.
(
a
+
b
+
c
)
(
a
2
−
a
b
−
a
c
+
b
2
−
b
c
+
c
2
)
(i)
(
2
a
3
−
3
a
b
c
+
b
3
+
c
3
)
(ii)
(
a
3
−
6
a
b
c
+
b
3
+
c
3
)
(iii)
(
−
3
a
b
c
+
b
3
+
c
3
)
(iv)
(
a
3
−
3
a
b
c
+
b
3
+
c
3
)
(v)
(
a
3
+
b
3
+
c
3
)
Question
12
12.
If
(
a
+
b
)
=
8
,
a
b
=
12
, find
(
a
3
+
b
3
)
(i)
225
(ii)
226
(iii)
223
(iv)
222
(v)
224
Question
13
13.
If
(
x
+
1
x
)
=
8
,
find the value of
(
x
2
+
1
x
2
)
(i)
63
(ii)
61
(iii)
59
(iv)
64
(v)
62
Question
14
14.
If
(
a
4
+
b
4
)
=
1921
,
a
b
=
30
, find
(
a
+
b
)
(i)
14
(ii)
12
(iii)
11
(iv)
8
(v)
10
Question
15
15.
The value of
504
✕
504
is
(i)
254017
(ii)
254015
(iii)
254016
(iv)
254019
(v)
254013
Question
16
16.
If
(
a
−
b
)
=
1
,
a
b
=
12
, find
(
a
3
−
b
3
)
(i)
38
(ii)
39
(iii)
36
(iv)
34
(v)
37
Question
17
17.
(
2
a
−
3
b
)
2
(i)
(
5
a
2
−
12
a
b
+
9
b
2
)
(ii)
(
4
a
2
−
9
a
b
+
9
b
2
)
(iii)
(
4
a
2
−
12
a
b
+
9
b
2
)
(iv)
(
3
a
2
−
12
a
b
+
9
b
2
)
(v)
(
4
a
2
−
14
a
b
+
9
b
2
)
Question
18
18.
(
a
+
b
)
2
(i)
(
a
2
−
a
b
+
b
2
)
(ii)
(
a
2
+
5
a
b
+
b
2
)
(iii)
(
a
2
+
2
a
b
+
b
2
)
(iv)
(
2
a
b
+
b
2
)
(v)
(
2
a
2
+
2
a
b
+
b
2
)
Question
19
19.
(
−
5
a
+
2
b
+
3
c
)
(
25
a
2
+
10
a
b
+
15
a
c
+
4
b
2
−
6
b
c
+
9
c
2
)
(i)
(
−
126
a
3
+
90
a
b
c
+
8
b
3
+
27
c
3
)
(ii)
(
−
124
a
3
+
90
a
b
c
+
8
b
3
+
27
c
3
)
(iii)
(
−
125
a
3
+
90
a
b
c
+
8
b
3
+
27
c
3
)
(iv)
(
−
125
a
3
+
87
a
b
c
+
8
b
3
+
27
c
3
)
(v)
(
−
125
a
3
+
92
a
b
c
+
8
b
3
+
27
c
3
)
Question
20
20.
(
−
3
a
−
3
b
)
(
−
3
a
+
3
b
)
(i)
(
9
a
2
−
11
b
2
)
(ii)
(
10
a
2
−
9
b
2
)
(iii)
(
8
a
2
−
9
b
2
)
(iv)
(
9
a
2
−
6
b
2
)
(v)
(
9
a
2
−
9
b
2
)
Question
21
21.
If
(
a
+
b
+
c
)
=
20
,
(
a
b
+
a
c
+
b
c
)
=
131
, find
(
a
2
+
b
2
+
c
2
)
(i)
136
(ii)
138
(iii)
137
(iv)
141
(v)
139
Question
22
22.
If
(
x
−
1
x
)
=
7
,
find the value of
(
x
4
+
1
x
4
)
(i)
2600
(ii)
2598
(iii)
2599
(iv)
2597
(v)
2602
Question
23
23.
(
a
+
b
+
c
)
2
(i)
(
a
2
−
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(ii)
(
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iii)
(
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iv)
(
a
2
+
5
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(v)
(
2
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
Question
24
24.
If
(
a
−
b
)
=
2
,
a
b
=
24
, find
(
a
2
−
b
2
)
(i)
19
(ii)
18
(iii)
21
(iv)
20
(v)
23
Question
25
25.
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(i)
(
2
a
3
−
b
3
)
(ii)
(
a
3
−
b
3
)
(iii)
(
a
3
−
3
b
3
)
(iv)
(
a
3
+
2
b
3
)
(v)
(
−
b
3
)
Assignment Key
1) (i)
2) (i)
3) (ii)
4) (ii)
5) (ii)
6) (ii)
7) (iv)
8) (i)
9) (ii)
10) (ii)
11) (iv)
12) (v)
13) (v)
14) (iii)
15) (iii)
16) (v)
17) (iii)
18) (iii)
19) (iii)
20) (v)
21) (ii)
22) (iii)
23) (ii)
24) (iv)
25) (ii)
