NCERT Solutions for Exercise 2.5 Class 9 Maths Chapter 2 - Polynomials

NCERT Solutions for Exercise 2.5 Class 9 Maths Chapter 2 - Polynomials

NCERT Solutions for Class 9 Maths chapter 2 exercise 2.5 introduces us to many identities which are covered in the whole exercise. An algebraic identity is an algebraic equation that is true for all values of the variables occurring in it. NCERT solutions for Class 9 Maths chapter 2 exercise 2.5 includes a variety of problems related to the application of all the algebraic identities in the question. In exercise 2.5 Class 9 Maths a lot of problems which also includes real-life application.

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Overall NCERT solutions for Class 9 Maths chapter 2 exercise 2.5 is the most important exercise as it is the base for the most important branch of mathematics called algebra. Exercise 2.5 Class 9 Maths includes the identities with two variables as well as three variables. Along with Class 9 Maths chapter 2 exercise 2.5, the following exercises are also present.

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  • Polynomial exercise 2.1
  • Polynomial exercise 2.2
  • Polynomial exercise 2.3
  • Polynomial exercise 2.4

Polynomials Class 9 Chapter 2 Exercise: 2.5

Q1 (i) Use suitable identities to find the following product:

Answer:

We will use identity



Put





Therefore, is equal to

Q1 (ii) Use suitable identities to find the following product:

Answer:

We will use identity



Put





Therefore, is equal to

Q1 (iii) Use suitable identities to find the following product:

Answer:

We can write as



We will use identity



Put





Therefore, is equal to

Q1 (iv) Use suitable identities to find the following product:

Answer:

We will use identity



Put





Therefore, is equal to

Q1 (v) Use suitable identities to find the following product:

Answer:

We can write as



We will use identity



Put





Therefore, is equal to

Q2 (i) Evaluate the following product without multiplying directly:

Answer:

We can rewrite as



We will use identity



Put





Therefore, value of is

Q2 (ii) Evaluate the following product without multiplying directly:

Answer:

We can rewrite as



We will use identity



Put





Therefore, value of is

Q2 (iii) Evaluate the following product without multiplying directly:

Answer:

We can rewrite as



We will use identity



Put





Therefore, value of is

Q3 (i) Factorise the following using appropriate identities:

Answer:

We can rewrite as



Using identity

Here,

Therefore,

Q3 (ii) Factorise the following using appropriate identities:

Answer:

We can rewrite as



Using identity

Here,

Therefore,

Q3 (iii) Factorise the following using appropriate identities:

Answer:

We can rewrite as



Using identity

Here,

Therefore,

Q4 (i) Expand each of the following, using suitable identities:

Answer:

Given is

We will Use identity



Here,

Therefore,



Q4 (ii) Expand each of the following, using suitable identities:

Answer:

Given is

We will Use identity



Here,

Therefore,



Q4 (iii) Expand each of the following, using suitable identities:

Answer:

Given is

We will Use identity



Here,

Therefore,



Q4 (iv) Expand each of the following, using suitable identities:

Answer:

Given is

We will Use identity



Here,

Therefore,



Q4 (v) Expand each of the following, using suitable identities:

Answer:

Given is

We will Use identity



Here,

Therefore,



Q4 (vi) Expand each of the following, using suitable identities:

Answer:

Given is

We will Use identity



Here,

Therefore,



Q5 (i) Factorise:

Answer:

We can rewrite as



We will Use identity



Here,

Therefore,



Q5 (ii) Factorise:

Answer:

We can rewrite as



We will Use identity



Here,

Therefore,



Q6 (i) Write the following cubes in expanded form:

Answer:

Given is

We will use identity



Here,

Therefore,



Q6 (ii) Write the following cube in expanded form:

Answer:

Given is

We will use identity



Here,

Therefore,



Q6 (iii) Write the following cube in expanded form:

Answer:

Given is

We will use identity



Here,

Therefore,



Q6 (iv) Write the following cube in expanded form:

Answer:

Given is

We will use identity



Here,

Therefore,



Q7 (i) Evaluate the following using suitable identities:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q7 (ii) Evaluate the following using suitable identities:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q7 (iii) Evaluate the following using suitable identities:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q8 (i) Factorise the following:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q8 (ii) Factorise the following:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q8 (iii) Factorise the following:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q8 (iv) Factorise the following:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q8 (v) Factorise the following:

Answer:

We can rewrite as



We will use identity



Here,

Therefore,



Q9 (i) Verify:

Answer:

We know that



Now,









Hence proved.

Q9 (ii) Verify:

Answer:

We know that



Now,









Hence proved.

Q10 (i) Factorise the following:

Answer:

We know that



Now, we can write as



Here,

Therefore,



Q10 (ii) Factorise the following:

Answer:

We know that



Now, we can write as



Here,

Therefore,



Q11 Factorise:

Answer:

Given is

Now, we know that



Now, we can write as



Here,

Therefore,



Q12 Verify that

Answer:

We know that



Now, multiply and divide the R.H.S. by 2







Hence proved.

Q13 If , show that .

Answer:

We know that



Now, It is given that

Therefore,







Hence proved.

Q14 (i) Without actually calculating the cubes, find the value of each of the following:

Answer:

Given is

We know that

If then ,

Here,



Therefore,



Therefore, value of is

Q14 (ii) Without actually calculating the cubes, find the value of the following:

Answer:

Given is

We know that

If then ,

Here,



Therefore,



Therefore, value of is

Q15 (i) Give possible expressions for the length and breadth of the following rectangle, in which its area is given:

Answer:

We know that

Area of rectangle is =

It is given that area =

Now, by splitting middle term method






Therefore, two answers are possible

case (i) :- Length = and Breadth =

case (ii) :- Length = and Breadth =

Q15 (ii) Give possible expressions for the length and breadth of the following rectangle, in which its area is given:

Answer:

We know that

Area of rectangle is =

It is given that area =

Now, by splitting the middle term method







Therefore, two answers are possible

case (i) :- Length = and Breadth =

case (ii) :- Length = and Breadth =

Q16 (i) What are the possible expressions for the dimensions of the cuboid whose volumes is given below?

Volume :

Answer:

We know that

Volume of cuboid is =

It is given that volume =

Now,



Therefore,one of the possible answer is possible

Length = and Breadth = and Height =

Q16 (ii) What are the possible expressions for the dimensions of the cuboid whose volumes is given below?

Volume :

Answer:

We know that

Volume of cuboid is =

It is given that volume =

Now,











Therefore,one of the possible answer is possible

Length = and Breadth = and Height =

More About NCERT Solutions for Class 9 Maths Exercise 2.1

Class 9 Maths chapter 2 exercise 2 includes some of the basic problems in question one in which we have to apply the algebraic identities. Question two and question seven have problems based on splitting and applying identities. There are some problems based on identities in finding areas and volumes. Hence we can say that NCERT solutions for Class 9 Maths exercise 2.1 is a cluster of all types of questions from direct to hard. So this is the best source for practicing algebraic identities in order to make the base strong for whole algebra.

Also Read| Polynomials Class 9 Notes

Benefits of NCERT Solutions for Class 9 Maths Exercise 2.5

  • Class 9 Maths chapter 2 exercise 2.5 is the most important exercise of chapter 2

  • NCERT Class 9 Maths chapter 2 exercise 2.5, will be useful in chapters of Class 10 such as chapter 2 polynomial, chapter 3 linear equation with two variable and chapter 4 quadratic equation

  • NCERT Class 9 Maths chapter 2 exercise 2.5, will be useful in chapters of class 11 such as chapter 5 complex number and quadratic equation and chapter 6 linear inequalities

  • NCERT Class 9 Maths chapter 2 exercise 2.5, will be helpful in JEE Main as algebra is in the syllabus

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NCERT Solutions of Class 10 Subject Wise

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  • NCERT Exemplar Class 9 Maths
  • NCERT Exemplar Class 9 Science