📘 About Class 9 Maths Chapter 4 Exercise 4.3 Solutions
Class 9 Maths Chapter 4 Exercise 4.3 Solutions are based on the latest NCERT Ganita Manjari (2026) textbook. This exercise helps students apply algebraic identities to find squares, expand algebraic expressions, factorise suitable expressions, and verify identities. The solutions are presented in a clear, step-by-step format so that Class 9 students can understand the method and write accurate answers in their notebooks and examinations.
🎯 What You’ll Learn
Learn how to recognise the suitable algebraic identity, use identities to find squares, expand expressions involving two or three terms, factorise expressions, and verify algebraic identities step by step.
📝 Why This Exercise Matters
Exercise 4.3 strengthens students’ ability to recognise algebraic patterns and apply the right identity efficiently. These skills are useful for simplifying expressions, factorisation, and solving algebraic problems in later chapters.
📚 Important Concepts Covered
📑 Table of Contents
Quickly navigate to any question of Class 9 Maths Chapter 4 Exercise 4.3 Solutions using the links below.
📝 Question 1
Find the squares using suitable algebraic identities.
🧮 Question 2
Factorise the following expressions.
⭐ Learn Before You Solve
Before solving Class 9 Maths Chapter 4 Exercise 4.3, learn how to identify the correct algebraic identity. Choosing the right identity first makes calculations easier, reduces mistakes, and helps you solve NCERT questions much faster.
① Rewrite First
Rewrite the given number or expression into a simple form before solving.
117 = 100 + 10 + 7
198 = 200 − 2
1104 = 1100 + 4
② Choose the Identity
✔ Two terms → (a + b)²
✔ Difference → (a − b)²
✔ Three terms → (a + b + c)²
③ Solve Carefully
Expand every term step by step. Don’t forget the cross terms like 2ab, 2bc and 2ca while using (a + b + c)².
💡 Quick Success Tips
- Always identify the suitable identity before starting the calculation.
- Write every intermediate step instead of solving mentally.
- For three-term expressions, never miss any cross-product term.
- After solving, compare your answer with the original expression to check correctness.
📝 Class 9 Maths Chapter 4 Exercise 4.3 Solutions
Solve every question of Class 9 Maths Chapter 4 Exercise 4.3 with simple, step-by-step NCERT Ganita Manjari (2026) solutions prepared in the latest CBSE answer-writing format.
Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier.
b = 10
c = 7
= 10000 + 100 + 49 + 2000 + 140 + 1400
= 13689
b = 2
= 6400 − 320 + 4
= 6084
b = 2
= 40000 − 800 + 4
= 39204
b = 10
c = 4
= 40000 + 100 + 16 + 4000 + 80 + 1600
= 45796
b = 4
= 1210000 + 8800 + 16
= 1218816
b = 20
= 1210000 + 44000 + 400
= 1254400
Factor using suitable identities:
2ab = 24y
b2 = 9
b = 3
=
(4y − 3)2
2ab = 6st
b2 = 4t2
b = 2t
=
( 3 2 s + 2t )2
=
( 3 2 s + 2t )2
2ab = mk 3
b² = k2 4
b = k 2
2ab = 2
b2 = 16 p2
b = 4 p
= 2 × 1
= 2 ✓
=
( p 4 − 4 p )2
= (x + y + z)2
= (3a − 2b + c)2
= (3a − 2b + c)2
= p2 + (3q)2 + (7r)2
+ 2(p)(3q) + 2(3q)(7r) + 2(7r)(p)
= p2 + 9q2 + 49r2 + 6pq + 42qr + 14pr
= p2 + 9q2 + 49r2 + 6pq + 42qr + 14pr
= (3x)2 + (−2y)2 + (4z)2
+ 2(3x)(−2y) + 2(−2y)(4z) + 2(4z)(3x)
= 9x2 + 4y2 + 16z2 − 12xy − 16yz + 24xz
= 9x2 + 4y2 + 16z2 − 12xy − 16yz + 24xz
(a − b + c)2 = a2 + b2 + c2 − 2ab + 2ac − 2bc
(a − b − c)2 = a2 + b2 + c2 − 2ab − 2ac + 2bc
= 3a2 + 3b2 + 3c2 − 2ab − 2ac − 2bc
RHS = 2a2 + 2b2 + 2c2
Therefore,
LHS ≠ RHS
📚 Continue Learning
Continue learning Class 9 Maths Chapter 4 Exploring Algebraic Identities by moving to the previous or next exercise, or explore solutions from other NCERT Class 9 Maths chapters.
🚀 Quick Revision Dashboard
Revise the important concepts of Class 9 Maths Chapter 4 Exercise 4.3 Solutions in just a few minutes. This quick revision guide will help you identify the correct algebraic identity, avoid common mistakes, and solve NCERT questions confidently in the CBSE examination.
📌 Identity Selection Guide
| 100 + 10 + 7 | → (a + b + c)² |
| 200 − 2 | → (a − b)² |
| 1100 + 4 | → (a + b)² |
| a² − b² | → (a + b)(a − b) |
❌ Common Mistakes
- Choosing the wrong identity.
- Not rewriting the number first.
- Missing 2ab, 2bc or 2ca.
- Making sign mistakes in (a − b)².
- Skipping intermediate steps.
📖 Formula Sheet
(a − b)2 = a2 − 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
a2 − b2 = (a + b)(a − b)
🎯 CBSE Exam Tips
- Rewrite every number into a convenient form before applying an identity.
- Identify the correct identity first, then substitute the values.
- Write every calculation step clearly to score full marks.
- Always check the signs while using (a − b)².
- Revise all four algebraic identities before attempting Exercise 4.3.
❓ Frequently Asked Questions
Find quick answers to the most common doubts related to Class 9 Maths Chapter 4 Exercise 4.3 Solutions. These FAQs will help you understand algebraic identities, choose the correct identity, and prepare better for your CBSE Class 9 Mathematics examination.
What is the main concept of Class 9 Maths Chapter 4 Exercise 4.3?
Exercise 4.3 focuses on the application of algebraic identities. Students learn to find squares quickly, expand algebraic expressions, factorise perfect square expressions, and verify identities using standard formulas.
Which algebraic identities are used in Exercise 4.3?
The most important identities are (a + b)², (a − b)², (a + b + c)², and a² − b² = (a + b)(a − b). Choosing the correct identity is the key to solving every question accurately.
How can I identify the correct algebraic identity?
First rewrite the given number or expression into a suitable form. For example, write 198 = 200 − 2 or 117 = 100 + 10 + 7. Then compare it with the standard identities and apply the matching one.
Are these Class 9 Maths Chapter 4 Exercise 4.3 solutions based on the latest NCERT book?
Yes. All solutions are prepared according to the latest NCERT Ganita Manjari (2026) textbook and follow the current CBSE Class 9 Mathematics syllabus and answer-writing format.
Is Exercise 4.3 important for the CBSE Class 9 exam?
Yes. Exercise 4.3 is one of the most important exercises in Chapter 4 because it develops the ability to apply algebraic identities correctly. These concepts are frequently used in school examinations and also form the foundation for higher algebra in future classes.
🔗 Useful Learning Resources
Explore these trusted resources to strengthen your understanding of Class 9 Maths Chapter 4 Exercise 4.3 and continue your learning journey.
🏛 Official Resources
📚 Maths Gurukulam Resources
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These Class 9 Maths Chapter 4 Exercise 4.3 Solutions are carefully prepared according to the latest NCERT Ganita Manjari (2026) and the CBSE curriculum. Every solution follows a clear, step-by-step approach designed to strengthen conceptual understanding, improve problem-solving skills, and help students perform confidently in school and board examinations.