Algebraic Identities - Exercise 4.4 - Extra Documents & Tests for Class 9

 Page 1


?        
  
     
Q u e s t i o n : 4 1
Find the following products:
i
(3x + 2y) (9x
2
 - 6xy + 4y
2
)
ii
(4x - 5y) (16x
2
 + 20xy + 25y
2
)
iii
(7p
4
 + q) (49p
8
 - 7p
4
q + q
2
)
iv
x
2
+2y 
x
2
4
-xy + 4y
2
v
3
x
-
5
y
 
9
x
2
+
25
y
2
+
15
xy
vi
3 +
5
x
 9 -
15
x
+
25
x
2
( )
( )
( )
( )
( )
( )
Page 2


?        
  
     
Q u e s t i o n : 4 1
Find the following products:
i
(3x + 2y) (9x
2
 - 6xy + 4y
2
)
ii
(4x - 5y) (16x
2
 + 20xy + 25y
2
)
iii
(7p
4
 + q) (49p
8
 - 7p
4
q + q
2
)
iv
x
2
+2y 
x
2
4
-xy + 4y
2
v
3
x
-
5
y
 
9
x
2
+
25
y
2
+
15
xy
vi
3 +
5
x
 9 -
15
x
+
25
x
2
( )
( )
( )
( )
( )
( )
vii
2
x
+3x 
4
x
2
+9x
2
-6
viii
3
x
-2x
2
 
9
x
2
+4x
4
-6x
ix
(1 - x) (1+ x + x
2
)
x
(1 + x) (1 - x + x
2
)
xi
(x
2
 - 1) (x
4
 + x
2
 + 1)
xii
(x
3
 + 1) (x
6
 - x
3 + 
1)
S o l u t i o n :
i In the given problem, we have to find the value of 
 Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
ii Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
iii Given
We shall use the identity 
We can rearrange the as
( )
( )
( )
( )
Page 3


?        
  
     
Q u e s t i o n : 4 1
Find the following products:
i
(3x + 2y) (9x
2
 - 6xy + 4y
2
)
ii
(4x - 5y) (16x
2
 + 20xy + 25y
2
)
iii
(7p
4
 + q) (49p
8
 - 7p
4
q + q
2
)
iv
x
2
+2y 
x
2
4
-xy + 4y
2
v
3
x
-
5
y
 
9
x
2
+
25
y
2
+
15
xy
vi
3 +
5
x
 9 -
15
x
+
25
x
2
( )
( )
( )
( )
( )
( )
vii
2
x
+3x 
4
x
2
+9x
2
-6
viii
3
x
-2x
2
 
9
x
2
+4x
4
-6x
ix
(1 - x) (1+ x + x
2
)
x
(1 + x) (1 - x + x
2
)
xi
(x
2
 - 1) (x
4
 + x
2
 + 1)
xii
(x
3
 + 1) (x
6
 - x
3 + 
1)
S o l u t i o n :
i In the given problem, we have to find the value of 
 Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
ii Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
iii Given
We shall use the identity 
We can rearrange the as
( )
( )
( )
( )
Hence the Product value of is 
iv Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
v Given
We shall use the identity 
We can rearrange the as
=
3
x
×
3
x
×
3
x
-
5
y
×
5
y
×
5
y
=
27
x
3
-
125
y
3
Hence the Product value of is 
vi Given
We shall use the identity ,
we can rearrange the as
( ) ( ) ( ) ( ) ( ) ( )
Page 4


?        
  
     
Q u e s t i o n : 4 1
Find the following products:
i
(3x + 2y) (9x
2
 - 6xy + 4y
2
)
ii
(4x - 5y) (16x
2
 + 20xy + 25y
2
)
iii
(7p
4
 + q) (49p
8
 - 7p
4
q + q
2
)
iv
x
2
+2y 
x
2
4
-xy + 4y
2
v
3
x
-
5
y
 
9
x
2
+
25
y
2
+
15
xy
vi
3 +
5
x
 9 -
15
x
+
25
x
2
( )
( )
( )
( )
( )
( )
vii
2
x
+3x 
4
x
2
+9x
2
-6
viii
3
x
-2x
2
 
9
x
2
+4x
4
-6x
ix
(1 - x) (1+ x + x
2
)
x
(1 + x) (1 - x + x
2
)
xi
(x
2
 - 1) (x
4
 + x
2
 + 1)
xii
(x
3
 + 1) (x
6
 - x
3 + 
1)
S o l u t i o n :
i In the given problem, we have to find the value of 
 Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
ii Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
iii Given
We shall use the identity 
We can rearrange the as
( )
( )
( )
( )
Hence the Product value of is 
iv Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
v Given
We shall use the identity 
We can rearrange the as
=
3
x
×
3
x
×
3
x
-
5
y
×
5
y
×
5
y
=
27
x
3
-
125
y
3
Hence the Product value of is 
vi Given
We shall use the identity ,
we can rearrange the as
( ) ( ) ( ) ( ) ( ) ( )
Hence the Product value of is 
vii Given
We shall use the identity ,
We can rearrange the as
Hence the Product value of is 
viii Given
We shall use the identity 
We can rearrange the as
3
x
-2x
2
3
x
2
+ 2x
2
2
-
3
x
2x
2
=
3
x
3
- 2x
2
3
=
3
x
3
x
3
x
- 2x
2
2x
2
2x
2
=
27
x
3
-8x
6
Hence the Product value of is 
ix Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
( )
(
( )
( )
( )
( )
)
( )
( )
( ) ( ) ( )
( ) ( ) ( )
Page 5


?        
  
     
Q u e s t i o n : 4 1
Find the following products:
i
(3x + 2y) (9x
2
 - 6xy + 4y
2
)
ii
(4x - 5y) (16x
2
 + 20xy + 25y
2
)
iii
(7p
4
 + q) (49p
8
 - 7p
4
q + q
2
)
iv
x
2
+2y 
x
2
4
-xy + 4y
2
v
3
x
-
5
y
 
9
x
2
+
25
y
2
+
15
xy
vi
3 +
5
x
 9 -
15
x
+
25
x
2
( )
( )
( )
( )
( )
( )
vii
2
x
+3x 
4
x
2
+9x
2
-6
viii
3
x
-2x
2
 
9
x
2
+4x
4
-6x
ix
(1 - x) (1+ x + x
2
)
x
(1 + x) (1 - x + x
2
)
xi
(x
2
 - 1) (x
4
 + x
2
 + 1)
xii
(x
3
 + 1) (x
6
 - x
3 + 
1)
S o l u t i o n :
i In the given problem, we have to find the value of 
 Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
ii Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
iii Given
We shall use the identity 
We can rearrange the as
( )
( )
( )
( )
Hence the Product value of is 
iv Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
v Given
We shall use the identity 
We can rearrange the as
=
3
x
×
3
x
×
3
x
-
5
y
×
5
y
×
5
y
=
27
x
3
-
125
y
3
Hence the Product value of is 
vi Given
We shall use the identity ,
we can rearrange the as
( ) ( ) ( ) ( ) ( ) ( )
Hence the Product value of is 
vii Given
We shall use the identity ,
We can rearrange the as
Hence the Product value of is 
viii Given
We shall use the identity 
We can rearrange the as
3
x
-2x
2
3
x
2
+ 2x
2
2
-
3
x
2x
2
=
3
x
3
- 2x
2
3
=
3
x
3
x
3
x
- 2x
2
2x
2
2x
2
=
27
x
3
-8x
6
Hence the Product value of is 
ix Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
( )
(
( )
( )
( )
( )
)
( )
( )
( ) ( ) ( )
( ) ( ) ( )
x Given
We shall use the identity 
We can rearrange the as
Hence the Product value of is 
xi Given
We shall use the identity 
We can rearrange the as
x
2
-1 x
2
2
+ x
2
(1)+(1)
2
Hence the Product value of is 
xii Given
We shall use the identity ,
We can rearrange the as
Hence the Product value of is .
Q u e s t i o n : 4 2
If x = 3 and y = - 1, find the values of each of the following using in identify:
i
(9y
2 
- 4x
2
) (81y
4
 +36x
2
y
2
 + 16x
4
)
ii
3
x
-
x
3
 
x
2
9
+
9
x
2
+1
iii
( )
[
( ) ( )
]
( )
( )
( )