Class 9 Maths Question Answers - Factorization of Algebraic Expressions

 Page 1


      
      
      
      
  
     
      
       
               
   
   
        
  
     
Question:87
If a + b + c = 0, then write the value of a
3
 + b
3
 + c
3
.
Page 2


      
      
      
      
  
     
      
       
               
   
   
        
  
     
Question:87
If a + b + c = 0, then write the value of a
3
 + b
3
 + c
3
.
Solution:
Recall the formula
When , we have
 
Question:88
If a
2
 + b
2
 + c
2
 = 20 and a + b + c = 0, find ab + bc + ca.
Solution:
Recall the formula
Given that
Then we have
Question:89
If a + b + c = 9 and ab + bc + ca = 40, find a
2
 + b
2
 +c
2
.
Solution:
Recall the formula
Given that
,
Then we have
Question:90
If a
2
 + b
2
 + c
2
 = 250 and ab + bc + ca = 3, find a + b + c.
Solution:
Recall the formula
Page 3


      
      
      
      
  
     
      
       
               
   
   
        
  
     
Question:87
If a + b + c = 0, then write the value of a
3
 + b
3
 + c
3
.
Solution:
Recall the formula
When , we have
 
Question:88
If a
2
 + b
2
 + c
2
 = 20 and a + b + c = 0, find ab + bc + ca.
Solution:
Recall the formula
Given that
Then we have
Question:89
If a + b + c = 9 and ab + bc + ca = 40, find a
2
 + b
2
 +c
2
.
Solution:
Recall the formula
Given that
,
Then we have
Question:90
If a
2
 + b
2
 + c
2
 = 250 and ab + bc + ca = 3, find a + b + c.
Solution:
Recall the formula
Given that
, 
Then we have
Question:91
Write the value of 25
3
 - 75
3 
+ 50
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
Question:92
Write the value of 48
3
 - 30
3
 - 18
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Page 4


      
      
      
      
  
     
      
       
               
   
   
        
  
     
Question:87
If a + b + c = 0, then write the value of a
3
 + b
3
 + c
3
.
Solution:
Recall the formula
When , we have
 
Question:88
If a
2
 + b
2
 + c
2
 = 20 and a + b + c = 0, find ab + bc + ca.
Solution:
Recall the formula
Given that
Then we have
Question:89
If a + b + c = 9 and ab + bc + ca = 40, find a
2
 + b
2
 +c
2
.
Solution:
Recall the formula
Given that
,
Then we have
Question:90
If a
2
 + b
2
 + c
2
 = 250 and ab + bc + ca = 3, find a + b + c.
Solution:
Recall the formula
Given that
, 
Then we have
Question:91
Write the value of 25
3
 - 75
3 
+ 50
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
Question:92
Write the value of 48
3
 - 30
3
 - 18
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes 
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
Question:93
Write the value of 
1
2
3
+
1
3
3
-
5
6
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that:
Recall the formula
When , this becomes
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
( ) ( ) ( )
Page 5


      
      
      
      
  
     
      
       
               
   
   
        
  
     
Question:87
If a + b + c = 0, then write the value of a
3
 + b
3
 + c
3
.
Solution:
Recall the formula
When , we have
 
Question:88
If a
2
 + b
2
 + c
2
 = 20 and a + b + c = 0, find ab + bc + ca.
Solution:
Recall the formula
Given that
Then we have
Question:89
If a + b + c = 9 and ab + bc + ca = 40, find a
2
 + b
2
 +c
2
.
Solution:
Recall the formula
Given that
,
Then we have
Question:90
If a
2
 + b
2
 + c
2
 = 250 and ab + bc + ca = 3, find a + b + c.
Solution:
Recall the formula
Given that
, 
Then we have
Question:91
Write the value of 25
3
 - 75
3 
+ 50
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
Question:92
Write the value of 48
3
 - 30
3
 - 18
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes 
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
Question:93
Write the value of 
1
2
3
+
1
3
3
-
5
6
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that:
Recall the formula
When , this becomes
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
( ) ( ) ( )
Question:94
Write the value of 30
3
 + 20
3
 - 50
3
.
Solution:
The given expression is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes
So, we have the new formula
, when .
Using the above formula, the value of the given expression is
Question:95
Factorize: x
4
 + x
2
 + 25.
Solution:
The given expression to be factorized is 
This can be written in the form
We cannot further factorize the expression. 
So, the required factorization is .