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CBSE Questions for Class 8 Maths Algebraic Expressions And Identities Quiz 2 - MCQExams.com
CBSE
Class 8 Maths
Algebraic Expressions And Identities
Quiz 2
State whether True or False.
Multiply:
−
2
3
a
7
b
2
and
−
9
4
a
b
5
.
The answer is
3
2
a
8
b
7
.
Report Question
0%
True
0%
False
Explanation
−
2
3
a
7
b
2
×
−
9
4
a
b
5
=
(
−
2
3
)
(
−
9
4
)
a
7
+
1
b
2
+
5
=
3
2
a
8
b
7
Multiply:
−
5
c
d
2
by
−
5
c
d
2
Report Question
0%
25
c
2
d
5
0%
25
c
3
d
4
0%
25
c
2
d
3
0%
25
c
2
d
4
Explanation
−
5
c
d
2
×
−
5
c
d
2
=
(
−
5
)
(
−
5
)
c
1
+
1
d
2
+
2
=
25
c
2
d
4
Multiply:
2
3
a
b
by
−
1
4
a
2
b
Report Question
0%
−
1
6
a
3
b
3
0%
−
1
6
a
3
b
2
0%
−
1
6
a
4
b
2
0%
−
1
6
a
3
b
4
Explanation
2
3
a
b
×
−
1
4
a
2
b
=
2
3
(
−
1
4
)
a
1
+
2
b
1
+
1
=
−
2
12
a
3
b
2
State whether True or False.
Multiply:
4
a
and
6
a
+
7
.
The answer is
24
a
2
+
28
a
.
Report Question
0%
True
0%
False
Explanation
4
a
×
(
6
a
+
7
)
=
24
a
2
+
28
a
State whether True or False.
Multiply:
2
a
2
−
5
a
−
4
and
−
3
a
.
The anwser is
−
6
a
3
+
15
a
2
+
12
a
.
Report Question
0%
True
0%
False
Explanation
(
2
a
2
−
5
a
−
4
)
×
(
−
3
a
)
=
2
a
2
(
−
3
a
)
−
5
a
(
−
3
a
)
−
4
(
−
3
a
)
=
2
(
−
3
)
a
2
+
1
−
(
5
)
(
−
3
)
a
1
+
1
−
4
(
−
3
)
a
=
−
6
a
3
+
15
a
2
+
12
a
Use identities to solve:
(
97
)
2
Report Question
0%
9
,
659
0%
9
,
409
0%
9
,
009
0%
9
,
209
Explanation
(
97
)
2
=
(
100
−
3
)
2
using,
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
=
(
100
)
2
−
2
(
100
)
3
+
(
3
)
2
=
10000
−
600
+
9
=
9409
Simplify:
x
2
(
3
−
5
y
2
)
+
x
(
x
y
2
−
3
x
)
−
2
y
(
y
−
2
x
2
y
)
Report Question
0%
6
x
2
−
2
y
2
−
3
x
2
y
0%
6
x
2
0%
3
x
2
y
0%
−
2
y
2
Explanation
We have to simplify
x
2
(
3
−
5
y
2
)
+
x
(
x
y
2
−
3
x
)
−
2
y
(
y
−
2
x
2
y
)
=
3
x
2
−
5
x
2
y
2
+
x
2
y
2
−
3
x
2
−
2
y
2
+
4
x
2
y
2
=
(
3
x
2
−
3
x
2
)
+
(
−
5
x
2
y
2
+
x
2
y
2
+
4
x
2
y
2
)
−
2
y
2
=
0
−
2
y
2
=
−
2
y
2
.
Hence given expression simplified to
−
2
y
2
Use the identity
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
to evaluate:
33
×
27
.
Report Question
0%
891
0%
881
0%
981
0%
841
Explanation
We know,
33
×
27
=
(
30
+
3
)
×
(
30
−
3
)
.
Applying the formula
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
,
where
a
=
30
,
b
=
3
,
we get,
33
×
27
=
(
30
+
3
)
×
(
30
−
3
)
=
30
2
−
3
2
=
900
−
9
=
891
.
Therefore, option
A
is correct.
Use the identity
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
to evaluate:
21
×
19
.
Report Question
0%
389
0%
399
0%
289
0%
429
Explanation
We know,
21
×
19
=
(
20
+
1
)
×
(
20
−
1
)
.
Applying the formula
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
,
where
a
=
20
,
b
=
1
,
we get,
21
×
19
=
(
20
+
1
)
×
(
20
−
1
)
=
20
2
−
1
2
=
400
−
1
=
399
.
Therefore, option
B
is correct.
Solve for
x
:
(
502
)
2
Report Question
0%
2
,
52
,
004
0%
2
,
62
,
104
0%
2
,
22
,
004
0%
2
,
52
,
864
Explanation
(
502
)
2
=
(
500
+
2
)
2
using,
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
=
(
500
)
2
+
2
(
500
)
(
2
)
+
(
2
)
2
=
250000
+
2000
+
4
=
252004
Use identities to evaluate:
(
101
)
2
Report Question
0%
11
,
601
0%
12
,
761
0%
10
,
111
0%
10
,
201
Explanation
(
101
)
2
=
(
100
+
1
)
2
using,
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
=
(
100
)
2
+
2
(
100
)
(
1
)
+
1
2
=
10000
+
200
+
1
=
10201
If
49
x
2
−
b
=
(
7
x
+
1
2
)
(
7
x
−
1
2
)
, then the value of
b
is :
Report Question
0%
0
0%
1
√
2
0%
1
4
0%
1
2
Explanation
(
7
x
+
1
2
)
(
7
x
−
1
2
)
=
49
x
2
−
b
⇒
49
x
2
−
1
4
=
49
x
2
−
b
(
∵
(
a
−
b
)
(
a
+
b
)
=
a
2
−
b
2
)
⇒
b
=
1
4
Option C is correct.
Evaluate using the expansion of
(
a
+
b
)
2
or
(
a
−
b
)
2
:
(
92
)
2
Report Question
0%
8444
0%
8464
0%
8474
0%
8414
Explanation
Given:
92
2
=
(
90
+
2
)
2
It is in the form of
(
a
+
b
)
2
, where
a
=
90
,
b
=
2
.
Applying the formula
(
a
+
b
)
2
=
a
2
+
b
2
+
2
a
b
we get,
92
2
=
(
90
+
2
)
2
=
90
2
+
2
2
+
2
×
90
×
2
=
8100
+
4
+
360
=
8464
Evaluate using expansion of
(
a
+
b
)
2
or
(
a
−
b
)
2
:
(
188
)
2
Report Question
0%
35444
0%
35484
0%
35344
0%
35384
Explanation
188
2
=
(
200
−
12
)
2
It is the form of
(
a
−
b
)
2
, where
a
=
200
,
b
=
12
Applying the formula
(
a
−
b
)
2
=
a
2
+
b
2
−
2
a
b
188
2
=
(
200
−
12
)
2
=
200
2
+
12
2
−
2
×
200
×
12
=
40000
+
144
−
4800
=
35344
Obtain the product of
2
,
4
y
,
8
y
2
,
16
y
3
Report Question
0%
1045
y
5
0%
1024
y
6
0%
1634
y
3
0%
102
y
5
Explanation
Product of
2
,
4
y
,
8
y
2
,
16
y
3
=
(
2
)
×
(
4
y
)
×
(
8
y
2
)
×
(
16
y
3
)
=
2
×
4
×
8
×
16
×
y
(
1
+
2
+
3
)
[
∵
a
m
×
a
n
=
a
m
+
n
]
=
1024
y
6
The product of
2
3
x
y
and
3
2
x
z
is equal to
Report Question
0%
1
6
xyz
0%
x
2
y
z
0%
6
x
2
y
z
0%
none of these
Explanation
2
3
x
y
×
3
2
x
z
=
x
2
y
z
Obtain the product of
a
,
−
a
2
,
a
3
Report Question
0%
a
5
0%
−
a
6
0%
a
3
0%
−
a
5
Explanation
a
,
a
2
,
a
3
=
(
a
)
×
(
−
a
2
)
×
(
a
3
)
=
−
a
6
Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
x
y
,
2
x
2
y
,
2
x
y
2
Report Question
0%
16
x
3
y
4
0%
4
x
2
y
3
0%
4
x
4
y
4
0%
4
x
2
y
2
Explanation
Given:
x
y
,
2
x
2
y
,
2
x
y
2
Volume
=
l
×
b
×
h
=
(
x
y
×
2
x
2
y
×
2
x
y
2
)
=
4
x
4
y
4
Find the product of
4
p
,
0
Report Question
0%
4
4
0%
1
0%
4
p
0%
0
Explanation
4
p
×
(
0
)
=
0
Obtain the volume of rectangular boxes with the given length, breadth and height respectively.
2
p
,
4
q
,
8
r
Report Question
0%
64
p
q
r
0%
16
p
q
r
0%
32
p
q
r
0%
8
p
r
+
r
Explanation
Given :
l
,
b
,
h
of the rectangular box respectively are:
2
p
,
4
q
,
8
r
Volume
=
l
×
b
×
h
=
(
2
×
4
×
8
)
p
q
r
=
64
p
q
r
Obtain the product of
a
,
2
b
,
3
c
,
6
a
b
c
Report Question
0%
36
a
2
b
2
c
3
0%
36
a
3
b
2
c
2
0%
36
a
2
b
2
c
2
0%
36
a
2
b
3
c
2
Explanation
a
,
2
b
,
3
c
,
6
a
b
c
=
(
a
)
×
(
2
b
)
×
(
3
c
)
×
(
6
a
b
c
)
=
36
a
2
b
2
c
2
Carry out the multiplication of the expressions of a given pair.
a
b
,
a
−
b
Report Question
0%
a
b
−
b
0%
a
2
b
+
a
b
0%
a
b
−
a
b
2
0%
a
2
b
−
a
b
2
Explanation
Given:
a
b
,
a
−
b
=
a
b
×
(
a
−
b
)
=
a
b
×
a
−
a
b
×
b
=
a
2
b
−
a
b
2
Simplify:
x
(
3
x
+
2
)
Report Question
0%
3
x
2
+
2
0%
3
x
+
2
0%
3
x
2
+
2
x
0%
3
x
2
+
x
Explanation
x
(
3
x
+
2
)
=
3
x
2
+
2
L
.
H
.
S
=
x
(
3
x
+
2
)
=
3
x
2
+
2
x
≠
R
.
H
.
S
The correct statement is
x
(
3
x
+
2
)
=
3
x
2
+
2
x
Carry out the multiplication of the given expressions.
a
+
b
,
7
a
2
b
2
Report Question
0%
a
3
b
2
−
7
a
2
b
3
0%
a
3
b
2
+
7
a
2
b
3
0%
7
a
3
b
3
+
7
a
2
b
2
0%
7
a
3
b
2
+
7
a
2
b
3
Explanation
Given:
a
+
b
,
7
a
2
b
2
Product
=
(
a
+
b
)
×
7
a
2
b
2
=
(
a
×
7
a
2
b
2
)
+
(
b
×
7
a
2
b
2
)
=
7
a
3
b
2
+
7
a
2
b
3
The value of
(
x
2
y
)
(
2
x
)
(
3
y
3
)
is
Report Question
0%
12
x
2
y
4
0%
6
x
3
y
4
0%
3
x
3
y
4
0%
x
3
y
4
Explanation
(
x
2
y
)
(
2
x
)
(
3
y
3
)
First:
(
2
)
(
3
)
=
6
Then:
(
x
3
)
(
y
4
)
So,
(
x
2
y
)
(
2
x
)
(
3
y
3
)
=
6
x
3
y
4
(
a
+
b
)
2
−
(
a
−
b
)
2
will be equal to
2
a
b
:
Report Question
0%
True
0%
False
0%
Ambiguous
0%
Data insufficient
Explanation
(
a
+
b
)
2
−
(
a
−
b
)
2
=
(
a
2
+
2
a
b
+
b
2
)
−
(
a
2
−
2
a
b
+
b
2
)
=
a
2
+
2
a
b
+
b
2
−
a
2
+
2
a
b
−
b
2
=
4
a
b
.
Hence, answer is
4
a
b
but not
2
a
b
.
Option
B
is correct.
Find the solution of
(
2
x
+
6
)
2
.
Report Question
0%
x
2
+
24
x
+
36
0%
4
x
2
+
24
x
+
6
0%
4
x
2
+
24
x
+
36
0%
4
x
2
−
24
x
+
36
Explanation
(
2
x
+
6
)
2
=
(
2
x
+
6
)
(
2
x
+
6
)
=
2
x
.2
x
+
2
x
.6
+
6.2
x
+
6.6
=
4
x
2
+
12
x
+
12
x
+
36
=
4
x
2
+
24
x
+
36
What is the coefficient of
x
when
−
x
+
6
is multiplied by
2
x
−
3
?
Report Question
0%
−
15
0%
15
0%
−
9
0%
9
Explanation
We have,
(
−
x
+
6
)
(
2
x
−
3
)
=
−
x
(
2
x
−
3
)
+
6
(
2
x
−
3
)
=
−
2
x
2
+
3
x
+
12
x
−
18
=
−
2
x
2
+
15
x
−
18
Hence, coefficient of
x
is
15
.
The coefficient of the product of two monomials is not equal to the product of their coefficient.
Report Question
0%
True
0%
False
0%
Sometimes
0%
Data insufficient
Explanation
The given statement is not true. We take an example.
2
x
,
3
y
are two monomials with coefficients
2
and
3
respectively.
Now,
(
2
x
)
(
3
y
)
=
6
x
y
, it is also monomial with coefficient
6
,
which is a product of
2
and
3.
Hence, option
B
is correct.
107
×
107
+
93
×
93
=
?
Report Question
0%
19578
0%
19418
0%
20098
0%
21908
0%
None of these
Explanation
107
×
107
+
93
×
93
=
107
2
+
93
2
=
(
100
+
7
)
2
+
(
100
−
7
)
2
=
2
×
[
(
100
)
2
+
7
2
]
...................... [Ref:
(
a
+
b
)
2
+
(
a
−
b
)
2
=
2
(
a
2
+
b
2
)
]
=
20098
0:0:2
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Practice Class 8 Maths Quiz Questions and Answers
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