Class 9 Exam > Class 9 Notes > Extra Documents & Tests for Class 9 > Algebraic Identities - Exercise 4.3
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Page 1
Q u e s t i o n : 2 2
Find the cube of each of the following binomials expressions:
i
1
x
+
y
3
ii
3
x
-
2
x
2
iii
2x +
3
x
iv
4 -
1
3x
S o l u t i o n :
In the given problem, we have to find cube of the binomial expressions
i Given
We shall use the identity
Here
By applying the identity we get
Page 2
Q u e s t i o n : 2 2
Find the cube of each of the following binomials expressions:
i
1
x
+
y
3
ii
3
x
-
2
x
2
iii
2x +
3
x
iv
4 -
1
3x
S o l u t i o n :
In the given problem, we have to find cube of the binomial expressions
i Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression is
ii Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression of is
iii Given
We shall use the identity .
Here ,
By applying identity we get
Hence cube of the binomial expression of is
Page 3
Q u e s t i o n : 2 2
Find the cube of each of the following binomials expressions:
i
1
x
+
y
3
ii
3
x
-
2
x
2
iii
2x +
3
x
iv
4 -
1
3x
S o l u t i o n :
In the given problem, we have to find cube of the binomial expressions
i Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression is
ii Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression of is
iii Given
We shall use the identity .
Here ,
By applying identity we get
Hence cube of the binomial expression of is
iv Given
We shall use the identity
Here
By applying in identity we get
Hence cube of the binomial expression of is .
Q u e s t i o n : 2 3
If a + b = 10 and ab = 21, find the value of a
3
+ b
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is .
Q u e s t i o n : 2 4
If a - b = 4 and ab = 21, find the value of a
3
-b
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Page 4
Q u e s t i o n : 2 2
Find the cube of each of the following binomials expressions:
i
1
x
+
y
3
ii
3
x
-
2
x
2
iii
2x +
3
x
iv
4 -
1
3x
S o l u t i o n :
In the given problem, we have to find cube of the binomial expressions
i Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression is
ii Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression of is
iii Given
We shall use the identity .
Here ,
By applying identity we get
Hence cube of the binomial expression of is
iv Given
We shall use the identity
Here
By applying in identity we get
Hence cube of the binomial expression of is .
Q u e s t i o n : 2 3
If a + b = 10 and ab = 21, find the value of a
3
+ b
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is .
Q u e s t i o n : 2 4
If a - b = 4 and ab = 21, find the value of a
3
-b
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is .
Q u e s t i o n : 2 5
If x +
1
x
= 5
, find the value of x
3
+
1
x
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is
Q u e s t i o n : 2 6
If x -
1
x
= 7
, find the value of x
3
-
1
x
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Page 5
Q u e s t i o n : 2 2
Find the cube of each of the following binomials expressions:
i
1
x
+
y
3
ii
3
x
-
2
x
2
iii
2x +
3
x
iv
4 -
1
3x
S o l u t i o n :
In the given problem, we have to find cube of the binomial expressions
i Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression is
ii Given
We shall use the identity
Here
By applying the identity we get
Hence cube of the binomial expression of is
iii Given
We shall use the identity .
Here ,
By applying identity we get
Hence cube of the binomial expression of is
iv Given
We shall use the identity
Here
By applying in identity we get
Hence cube of the binomial expression of is .
Q u e s t i o n : 2 3
If a + b = 10 and ab = 21, find the value of a
3
+ b
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is .
Q u e s t i o n : 2 4
If a - b = 4 and ab = 21, find the value of a
3
-b
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is .
Q u e s t i o n : 2 5
If x +
1
x
= 5
, find the value of x
3
+
1
x
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is
Q u e s t i o n : 2 6
If x -
1
x
= 7
, find the value of x
3
-
1
x
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is
Q u e s t i o n : 2 7
If x -
1
x
= 5
, find the value of x
3
-
1
x
3
S o l u t i o n :
In the given problem, we have to find the value of
Given
We shall use the identity
Here putting ,
Hence the value of is .
Q u e s t i o n : 2 8
If x
2
+
1
x
2
= 51, find the value of x
3
-
1
x
3
S o l u t i o n :
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