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Algebraic Identities - Exercise 4.3 | Extra Documents & Tests for Class 9 PDF Download

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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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