NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.3 | 2026-27

Think and Reflect 

Label the squares and rectangles in Fig. 4.4 so that it represents the identity.
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.

Solution:

Exercise Set 4.3

Question 1.

Find the following squares using one of the above calculations, whichever is easier.

(i) 1172

Solution:

1172 = (100 + 10 + 7)2

= 1002 + 102 + 72 + 2(100)(10) + 2(10)(7) + 2(7)(100)

[∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2be + 2ca]

= 10000 +100 + 49 + 2000 + 140 + 1400 = 13689

(ii) 782

Solution:
782 = (80 – 2)2 = 802 – 2 × 80 × 2 + 22
[∵(a – b)2 = a2 – 2ab + b2]
= 6400 – 320 + 4
= 6084     

(iii) 1982

Solution:
1982 = (200 – 2)2
= 2002 + 22 – 2 × 200 × 2
[∵(a – b)2 = a2 – 2ab + b2]
= 40000 – 800 + 4
= 39204

(iv) 2142

Solution:
2142 = (200 + 10 + 4)2
= 2002 + 102 + 42 + 2(200)(10) + 2(10)(4) + 2(4)(200)
[∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2be + 2ca]
= 40000 + 100 + 16 + 4000 + 80 + 1600
= 45796

(v) 11042

Solution:

11042 = (1000+ 100 + 4)2
= 10002 + 1002 + 42 + 2(1000) (100) + 2(100)(4) + 2(4)(1000)
[∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2be + 2ca]
= 1000000 + 10000 + 16 + 200000 + 800 + 8000
= 1218816

(vi) 11202

Solution:

11202 = (1000 + 100 + 20)2
= 10002 + 1002 + 202 + 2(1000)(100) + 2(100)(20) + 2(20)(1000)
[∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
= 1000000 + 10000 + 400 + 200000 + 4000 + 40000
= 1254400

Question 2.

Factor using suitable identities:

(i) 16y2 – 24y + 9

Solution:

16y2 – 24y + 9 = (4y)2 – 2 × (4y) × 3 + (3)2

= (4y – 3)2

[∵(a – b)2 = a2 – 2ab + b2]

(ii) 94s2 + 6st + 4t

Solution:

94s2 + 6st + 4t 

= 32S2 + 2 ×32S (2t) + (2t)2

= 32S+ 2t2

(iii) 𝑚2/9+𝑚𝑘/3+𝑘2/4+ 3nk + 2mn + 9n2

Solution:

Using the identity:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Here,

a = m/3, b = k/2, c = 3n

Therefore,

m²/9 + mk/3 + k²/4 + 3nk + 2mn + 9n²

= (m/3 + k/2 + 3n)²

Answer: (m/3 + k/2 + 3n)²

(iv) p²/16 − 2 + 16/p²

Solution:

(p/4)² − 2 × (p/4) × (4/p) + (4/p)²

= (p/4 − 4/p)²

[∵ (a − b)² = a² − 2ab + b²]

(v) 9a2 + 4b2 + c2 – 12ab + 6ac – 46c

Solution:

9a2 + 4b2 + c2 – 12ab + 6ac – 46c

= (3a)2 + (-2b)2 + (c)2 + 2(3a)(-2b) + 2(3a)(c) + 2(-2b)(c)

= [3a + (-2b) + c]2

= (3a – 2b + c)2

Question 3.
Expand the following using the identity.
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca:

(i) (p + 3q + 7r)2

Solution:

(p + 3q + 7r)2
= p2 + (3q)2 + (7r)2 + 2{p)(3q) + 2(3q)(7r) + 2(p)(7r)
= p2 + 9q2 + 49r2 + 6pq + 42 qr + 14pr

(ii) (3x – 2y + 4z)2

Solution:

(3x – 2y + 4z)2
= (3x)2 + (-2y)2 + (4z)2 + 2(3x)(-2y) + 2(-2y) + 2(-2y)(4z) + 2(3x)(4z)
= 9x2 + 4y2 + 16x2 – 12xy – 16yz + 24xz

Question 4.
Is this an identity?

(a + b − c)² + (a − b + c)² + (a − b − c)² = 2a² + 2b² + 2c²

Solution:

No, the given equation is not an identity.

Expanding the LHS, we get:

(a + b − c)² + (a − b + c)² + (a − b − c)²

= a² + b² + c² + 2ab − 2ac − 2bc

• a² + b² + c² − 2ab + 2ac − 2bc

• a² + b² + c² − 2ab − 2ac + 2bc

= 3a² + 3b² + 3c² − 2ab − 2ac − 2bc

The RHS is:

2a² + 2b² + 2c²

Since the LHS ≠ RHS, the equation is not true for all values of a, b and c.

Hence, the given equation is not an identity.

Benefits of Using Vedantu’s Class 9 Maths Chapter 4 Exercise 4.3 Solutions

The Class 9 Maths Chapter 4 Exercise 4.3 Solutions help students practise algebraic identities with clear, step-by-step explanations. 

Students can use the NCERT Maths Class 9 Chapter 4 Exercise 4.3 Solutions to:

• Understand each step: Follow the method used to solve every Exercise 4.3 Class 9 question.

• Apply identities correctly: Learn how to identify and use the appropriate algebraic identity in different problems.

• Check your answers: Compare your working with the Class 9 Maths Chapter 4 Exercise 4.3 Solutions to find and correct mistakes.

• Revise important concepts: Use the solutions as a quick reference while revising Chapter 4, Exploring Algebraic Identities.

• Build problem-solving confidence: Practising the Class 9 Maths NCERT Solutions Chapter 4 Exercise 4.3 helps students solve similar questions independently.

• Prepare for exams: Regular practice of Exercise 4.3 questions PDF improves accuracy and familiarity with algebraic identity-based problems.

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

CBSE Class 9 Maths Chapter 4 Exploring Algebraic Identities Study Materials

Additional Study Materials for Class 9 Maths