Exercise 2.5
NCERT solutions for Class 9 Maths Polynomials
NCERT Solutions for Class 9 Maths Polynomials
1. Use suitable identities to find the following products:
(i)
(ii) 
(iii) 
(iv) 
(v)
Ans. (i)
We know that
.
We need to apply the above identity to find the product
Therefore, we conclude that the productis
.
(ii)
We know that.
We need to apply the above identity to find the product
=
Therefore, we conclude that the productis
.
(iii)
We know that.
We need to apply the above identity to find the product
Therefore, we conclude that the productis
.
(iv)
We know that
.
We need to apply the above identity to find the product
Therefore, we conclude that the productis
.
(v) 
We know that.
We need to apply the above identity to find the product
Therefore, we conclude that the productis
.
2.Evaluate the following products without multiplying directly:
(i)
(ii)
(iii)
Ans. (i)
We can observe that, we can apply the identity
=10000+1000+21
=11021
Therefore, we conclude that the value of the product
is
.
(ii)
We can observe that, we can apply the identity
=10000-900+20
=9120
Therefore, we conclude that the value of the productis 
.
(iii) 
We can observe that, we can apply the identitywith respect to the expression
, to get
=10000-16
=9984
Therefore, we conclude that the value of the productis
.
3.Factorize the following using appropriate identities:
(i)
(ii)
(iii)
Ans. (i)
We can observe that, we can apply the identity
(ii)
We can observe that, we can apply the identity
(iii)
We can observe that, we can apply the identity
4.Expand each of the following, using suitable identities:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Ans. (i)
We know that
.
We need to apply the above identity to expand the expression.
(ii)
We know that.
We need to apply the above identity to expand the expression.
(iii)
We know that.
We need to apply the above identity to expand the expression.
(iv)
We know that.
We need to apply the above identity to expand the expression.
(v)
We know that.
We need to apply the above identity to expand the expression.
(vi)
We know that
.
NCERT Solutions for Class 9 Maths Exercise 2.5
5. Factorize:
(i)
(ii)
Ans. (i)
The expression 
can also be written as
We can observe that, we can apply the identitywith respect to the expression
, to get
Therefore, we conclude that after factorizing the expression, we get.
(ii)
We need to factorize the expression.
The expression 
can also be written as
We can observe that, we can apply the identitywith respect to the expression
, to get
Therefore, we conclude that after factorizing the expression, we get.
NCERT Solutions for Class 9 Maths Exercise 2.5
6. Write the following cubes in expanded form:
(i)
(ii)
(iii)
(iv)
Ans. (i)
We know that
.
Therefore, the expansion of the expressionis 
.
(ii)
We know that
.
Therefore, the expansion of the expressionis 
.
(iii)
We know that.
Therefore, the expansion of the expressionis
.
(iv)
We know that.
Therefore, the expansion of the expressionis
.
NCERT Solutions for Class 9 Maths Exercise 2.5
7. Evaluate the following using suitable identities:
(i)
(ii)
(iii)
Ans. (i)
Using identity,
=1000000-1-300(99)
=999999-29700
=970299
(ii)
Using identity
=1000000+8+600(102)
=1000008+61200
=1061208
(iii)
Using identity
=1000000000-8-6000(998)
=999999992-5988000
=994011992
NCERT Solutions for Class 9 Maths Exercise 2.5
8. Factorize each of the following:
(i)
(ii)
(iii)
(iv)
(v)
Ans.(i)
Using identitywithrespect to the expression
, we get
.
Therefore, after factorizing the expression, we get.
(ii)
Using identitywith respect to the expression
, we get
.
Therefore, after factorizing the expression, we get.
(iii)
The expression 
can also be written as
Using identitywith respect to the expression
, we get
.
Therefore, after factorizing the expression, we get.
(iv)
The expression 
can also be written as
Using identitywith respect to the expression
, we get
.
Therefore, after factorizing the expression, we get.
(v)
Using identitywith respect to the expression
, to get
.
Therefore, after factorizing the expression, we get.
NCERT Solutions for Class 9 Maths Exercise 2.5
9. Verify:
(i)
(ii)
Ans. (i)
We know that.
We know that
Therefore, the desired result has been verified.
(ii)
We know that.
We know that
Therefore, the desired result has been verified.
NCERT Solutions for Class 9 Maths Exercise 2.5
10. Factorize:
(i)
(ii)
Ans. (i)
We know that.
(ii)
We know that.
.
Therefore, we conclude that after factorizing the expression, we get
.
NCERT Solutions for Class 9 Maths Exercise 2.5
11. Factorize: 
Ans. 
We know that
.
Therefore, we conclude that after factorizing the expression, we get
.
NCERT Solutions for Class 9 Maths Exercise 2.5
12. Verify that
Ans. 
We know that.
And also, we know that.
Therefore, we can conclude that the desired result is verified.
NCERT Solutions for Class 9 Maths Exercise 2.5
13. If
, show that
.
Ans. We know that.
We need to substitutein
, to get
=(0)=
Therefore, the desired result is verified.
NCERT Solutions for Class 9 Maths Exercise 2.5
14.Without actually calculating the cubes, find the value of each of the following:
(i)
(ii)
Ans. (i)
Let 
and 
We know that, if 
then 
Here,
= 
(ii)
Let 
and 
We know that, if then
Here,
= 
NCERT Solutions for Class 9 Maths Exercise 2.5
15.Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i)
(ii)
Ans. (i)
The expression 
can also be written as 
Therefore, we can conclude that a possible expression for the length and breadth of a rectangle of area
is
.
(ii)
Therefore, we can conclude that a possible expression for the length and breadth of a rectangle of area
is
.
NCERT Solutions for Class 9 Maths Exercise 2.5
16.What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i)
(ii)
Ans. (i)
The expression 
can also be written as 
Therefore, we can conclude that a possible expression for the dimension of a cuboid of volume
is
.
(ii)
The expression 
can also be written as 
Therefore, we can conclude that a possible expression for the dimension of a cuboid of volume
is
.