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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
( )
[
( ) ( )
]
( )
( )
( )
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Nov 22, 2024 Last updated |
Document Description: Algebraic Identities - Exercise 4.4 for Class 9 2024 is part of Extra Documents & Tests for Class 9 preparation.
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Algebraic Identities - Exercise 4.4 Free PDF Download
The Algebraic Identities - Exercise 4.4 is an invaluable resource that delves deep into the core of the Class 9 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
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The importance of Algebraic Identities - Exercise 4.4 cannot be overstated, especially for Class 9 aspirants.
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Algebraic Identities - Exercise 4.4 Notes
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Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge
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