Factorization of Algebraic Expressions - Exercise 5.4 | Extra Documents & Tests for Class 9 PDF Download

 Page 1


      
      
       
      
          
        
            
      
      
      
Question:71
Factorize each of the following expressions:
a
3
 + 8b
3
 + 64c
3
 - 24abc
 
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:72
x
3 
- 8y
3
 + 27z
3
 + 18xyz
Solution:
The given expression to be factorized is
This can be written in the form
Page 2


      
      
       
      
          
        
            
      
      
      
Question:71
Factorize each of the following expressions:
a
3
 + 8b
3
 + 64c
3
 - 24abc
 
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:72
x
3 
- 8y
3
 + 27z
3
 + 18xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:73
27x
3
 - y
3
 - z
3
 - 9xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:74
1
27
x
3
-y
3
+125z
3
+5xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
Page 3


      
      
       
      
          
        
            
      
      
      
Question:71
Factorize each of the following expressions:
a
3
 + 8b
3
 + 64c
3
 - 24abc
 
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:72
x
3 
- 8y
3
 + 27z
3
 + 18xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:73
27x
3
 - y
3
 - z
3
 - 9xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:74
1
27
x
3
-y
3
+125z
3
+5xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:75
8x
3
 +27y
3
 - 216z
3
 + 108xyz
Solution:
The given expression to be factorized is
This can be written in the form 
Recall the formula 
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:76
125 + 8x
3
 - 27y
3
 + 90xy
Solution:
The given expression to be factorized is 
This can be written in the form 
Recall the formula 
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:77
8x
3
 - 125y
3
 + 180xy + 216
Solution:
The given expression to be factorized is
This can be written in the form
Page 4


      
      
       
      
          
        
            
      
      
      
Question:71
Factorize each of the following expressions:
a
3
 + 8b
3
 + 64c
3
 - 24abc
 
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:72
x
3 
- 8y
3
 + 27z
3
 + 18xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:73
27x
3
 - y
3
 - z
3
 - 9xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:74
1
27
x
3
-y
3
+125z
3
+5xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:75
8x
3
 +27y
3
 - 216z
3
 + 108xyz
Solution:
The given expression to be factorized is
This can be written in the form 
Recall the formula 
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:76
125 + 8x
3
 - 27y
3
 + 90xy
Solution:
The given expression to be factorized is 
This can be written in the form 
Recall the formula 
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:77
8x
3
 - 125y
3
 + 180xy + 216
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization is of is .
Question:78
Multiply:
i
x
2
 + y
2
 + z
2
 - xy + xz + yz by x + y - z
ii
x
2
 + 4y
2
 + z
3
 + 2xy + xz - 2yz by x - 2y - z
iii
x
2 
+ 4y
2
 + 2xy - 3x + 6y + 9 by x - 2y + 3
iv
9x
2
 + 25y
2
 + 15xy + 12x - 20y + 16 by 3x - 5y + 4
Solution:
i The given expression is
We have to multiply the above expression by .
The required product is
Recall the formula
Using the above formula, we have
ii The given expression is
We have to multiply the above expression by .
The required product is
Recall the formula
Using the above formula, we have
Page 5


      
      
       
      
          
        
            
      
      
      
Question:71
Factorize each of the following expressions:
a
3
 + 8b
3
 + 64c
3
 - 24abc
 
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:72
x
3 
- 8y
3
 + 27z
3
 + 18xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:73
27x
3
 - y
3
 - z
3
 - 9xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:74
1
27
x
3
-y
3
+125z
3
+5xyz
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:75
8x
3
 +27y
3
 - 216z
3
 + 108xyz
Solution:
The given expression to be factorized is
This can be written in the form 
Recall the formula 
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:76
125 + 8x
3
 - 27y
3
 + 90xy
Solution:
The given expression to be factorized is 
This can be written in the form 
Recall the formula 
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:77
8x
3
 - 125y
3
 + 180xy + 216
Solution:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
We cannot further factorize the expression.
So, the required factorization is of is .
Question:78
Multiply:
i
x
2
 + y
2
 + z
2
 - xy + xz + yz by x + y - z
ii
x
2
 + 4y
2
 + z
3
 + 2xy + xz - 2yz by x - 2y - z
iii
x
2 
+ 4y
2
 + 2xy - 3x + 6y + 9 by x - 2y + 3
iv
9x
2
 + 25y
2
 + 15xy + 12x - 20y + 16 by 3x - 5y + 4
Solution:
i The given expression is
We have to multiply the above expression by .
The required product is
Recall the formula
Using the above formula, we have
ii The given expression is
We have to multiply the above expression by .
The required product is
Recall the formula
Using the above formula, we have
iii The given expression is
We have to multiply the above expression by .
The required product is
Recall the formula
Using the above formula, we have
iii The given expression is
We have to multiply the above expression by .
The required product is
Recall the formula
Using the above formula, we have
Question:79
(3x - 2y)
3
 + (2y - 4z)
3
 + (4z - 3x)
3
Solution:
The given expression to be factorized is
Let , and . Then the given expression becomes
Note that
Recall the formula
When , this becomes
So, we have the new formula