Algebraic Identities - Exercise 4.4

# Algebraic Identities - Exercise 4.4 | Extra Documents & Tests for Class 9 PDF Download

``` 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
( )
[
( ) ( )
]
( )
( )
( )
```

## Extra Documents & Tests for Class 9

1 videos|228 docs|21 tests

## Extra Documents & Tests for Class 9

1 videos|228 docs|21 tests

### Up next

 Explore Courses for Class 9 exam

### Top Courses for Class 9

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;