Factorization of Algebraic Expressions - Exercise 5.3 | Extra Documents & Tests for Class 9 PDF Download

 Page 1


      
     
      
      
      
       
              
    
      
     
Question:60
Factorize:
64a
3
 + 125b
3
 + 240a
2
b + 300ab
2
 
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms,
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
Page 2


      
     
      
      
      
       
              
    
      
     
Question:60
Factorize:
64a
3
 + 125b
3
 + 240a
2
b + 300ab
2
 
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms,
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:61
125x
3
 - 27y
3
 - 225x
2
y + 135xy
2
Solution:
The given expression to be factorized is 
This can be written in the form 
Take common from the last two terms,. Then we get 
This can be written in the following form
Recall the formula for the cube of the difference of two numbers 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:62
8
27
x
3
+1 +
4
3
x
2
+2x
Solution:
The given expression to be factorized is
This can be written in the form
Take common from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:63
Page 3


      
     
      
      
      
       
              
    
      
     
Question:60
Factorize:
64a
3
 + 125b
3
 + 240a
2
b + 300ab
2
 
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms,
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:61
125x
3
 - 27y
3
 - 225x
2
y + 135xy
2
Solution:
The given expression to be factorized is 
This can be written in the form 
Take common from the last two terms,. Then we get 
This can be written in the following form
Recall the formula for the cube of the difference of two numbers 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:62
8
27
x
3
+1 +
4
3
x
2
+2x
Solution:
The given expression to be factorized is
This can be written in the form
Take common from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:63
8x
3
 + 27y
3
 + 36x
2
y + 54xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:64
a
3
 - 3a
2
b + 3ab
2
 - b
3
 + 8
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the third and fourth terms. Then we get
This can be written in the following form
Recall the formula for the cube of the difference of two numbers
Using the above formula, we have
This can be written in the following form
Recall the formula for the sum of two cubes
Using the above formula, we have
Page 4


      
     
      
      
      
       
              
    
      
     
Question:60
Factorize:
64a
3
 + 125b
3
 + 240a
2
b + 300ab
2
 
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms,
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:61
125x
3
 - 27y
3
 - 225x
2
y + 135xy
2
Solution:
The given expression to be factorized is 
This can be written in the form 
Take common from the last two terms,. Then we get 
This can be written in the following form
Recall the formula for the cube of the difference of two numbers 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:62
8
27
x
3
+1 +
4
3
x
2
+2x
Solution:
The given expression to be factorized is
This can be written in the form
Take common from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:63
8x
3
 + 27y
3
 + 36x
2
y + 54xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:64
a
3
 - 3a
2
b + 3ab
2
 - b
3
 + 8
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the third and fourth terms. Then we get
This can be written in the following form
Recall the formula for the cube of the difference of two numbers
Using the above formula, we have
This can be written in the following form
Recall the formula for the sum of two cubes
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:65
x
3
 + 8y
3
 + 6x
2
y + 12xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:66
8x
3
 + y
3
 + 12x
2
y + 6xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common 6xy from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:67
Page 5


      
     
      
      
      
       
              
    
      
     
Question:60
Factorize:
64a
3
 + 125b
3
 + 240a
2
b + 300ab
2
 
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms,
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization of is .
Question:61
125x
3
 - 27y
3
 - 225x
2
y + 135xy
2
Solution:
The given expression to be factorized is 
This can be written in the form 
Take common from the last two terms,. Then we get 
This can be written in the following form
Recall the formula for the cube of the difference of two numbers 
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:62
8
27
x
3
+1 +
4
3
x
2
+2x
Solution:
The given expression to be factorized is
This can be written in the form
Take common from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:63
8x
3
 + 27y
3
 + 36x
2
y + 54xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:64
a
3
 - 3a
2
b + 3ab
2
 - b
3
 + 8
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the third and fourth terms. Then we get
This can be written in the following form
Recall the formula for the cube of the difference of two numbers
Using the above formula, we have
This can be written in the following form
Recall the formula for the sum of two cubes
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:65
x
3
 + 8y
3
 + 6x
2
y + 12xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common from the last two terms. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:66
8x
3
 + y
3
 + 12x
2
y + 6xy
2
Solution:
The given expression to be factorized is 
This can be written in the form
Take common 6xy from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:67
8a
3 
+ 27b
3
 + 36a
2
b + 54ab
2
Solution:
The given expression to be factorized is
This can be written in the form
Take common from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the sum of two numbers
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:68
8a
3
 - 27b
3
 - 36a
2
b + 54ab
2
Solution:
The given expression to be factorized is 
This can be written in the form 
Take common – 18ab from the last two terms,. Then we get 
This can be written in the following form
Recall the formula for the cube of the difference of two numbers
Using the above formula, we have 
We cannot further factorize the expression. 
So, the required factorization is of is .
Question:69
x
3
 - 12x(x - 4) - 64
Solution:
The given expression to be factorized is 
This can be written in the form
Take common – 12x from the last two terms,. Then we get
This can be written in the following form
Recall the formula for the cube of the difference of two numbers
Using the above formula, we have
We cannot further factorize the expression.