NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2 | Exploring Algebraic Identities 2026-27

Think and Reflect

What if we replace b by – b in (a + b)2 = a2+ 2ab + b2?

Solution:

We get (a – b)2 = a2 – 2ab + b2, which is also an identity and can be used in ways similar to (a + b)2 = a2 + 2ab + b2

Exercise Set 4.2

Question 1.

Factor completely:

(i) 9x2 + 14xy + 16y2

Solution:

9x2 + 14xy + 16y2

= (3x)2 + 2 × (3x) × (4y) + (4y)2

= (3x + 4y)2 [∵ (a + b)2 = a2 + 2ab + b2]

(ii) 4s2 + 20st + 25t2

Solution:

4s2 + 20st + 25t2
= (2s)2 + 2 × (2s) × (5t) + (5t)2
= (2s + 5t)2 [∵ (a + b)2 = a2 + 2ab + b2]

(iii) 49x2 + 28xy + 4y2

Solution:

49x2 + 28xy + 4y2
= (7x)2 + 2 × (7x) × (2y) + (2y)2
= (7x + 2y)2 [∵ (a + b)2 = a2 + 2ab + b2]

(iv) 64p2 + 323 pq +49q2

Solution:

64p2 + 323 pq +49q2

= (8p)2 + 2 × (8p) × 23q+ 23q2

= (8p + 23q)2

(v) 3a2 + 4ab + 43 b2

Solution

3a² + 4ab + 4/3 b²
= 1/3(9a² + 12ab + 4b²)
= 1/3(3a + 2b)²

Answer: (3a + 2b)²/3

(vi) 95 s² + 6sv + 5v2

Solution

= 35s2+ 2 35s (√5v) + (√5v)2

(∵ 6 = 2 × 35 √5)

=  35 s + 5v2

[∵ (a + b)2 = a2 + 2ab + b2]

Question 2.

Find the values of the following using the identity (a – b)2 = a2 – 2ab + b2.

(i) (79)2

(ii) (193)2

(iii) (299)2

Solution:

(i) (79)2 = (80 – 1)2

= (80)2 + (1)2 – 2(80)(1)

[∵ (a – b)2 = a2 + b2 – 2ab]

= 6400 + 1 – 160

= 6401 – 160

= 6241

(ii) We have, (193)2 =(200 – 7)2

= (200)2 + (7)2 – 2(200) (7)

[∵ (a -b)2 = a2 + b2 – 2ab]

= 40000 + 49 – 2800

= 40049 – 2800

= 37249

(iii) We have (299)2 =(300 – 1)2

= (300)2 + (1)2 – 2(300) (1)

[∵ (a – b)2 = a2 + b2 – 2ab]

= 90000 + 1 – 600

= 90001 – 600

= 89401

How Vedantu’s Class 9 Maths Chapter 4 Exercise 4.2 Solutions Help Students?

Class 9 Maths Chapter 4 Exercise 4.2 solutions make it easier to understand the concepts and solve each question with a clear approach. 

Students can try the questions on their own first, then use the solutions to check their answers, understand difficult steps, and correct mistakes.

These NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2 are helpful for:

• Understanding concepts: Follow the steps to see how each question is solved.

• Clearing doubts: Revisit questions that seem difficult or confusing.

• Improving accuracy: Compare your working with the explained solutions.

• Revising quickly: Review important concepts from Class 9 Maths Chapter 4 Solutions Exercise 4.2 before tests and exams.

• Building confidence: Practise similar questions using the methods explained in the NCERT Class 9 Maths Chapter 4 Exercise 4.2 Solutions.

Regular practice, combined with these solutions as a reference, can help students develop stronger problem-solving skills and mathematical understanding.

Access Exercise-wise NCERT Solutions for Chapter 4 Maths Class 9

CBSE Class 9 Maths Chapter 4 Exploring Algebraic Identities Study Materials

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