📘 About Class 9 Maths Chapter 4 Exercise 4.2
Class 9 Maths Chapter 4 Exercise 4.2 is based on the concept of factorisation using algebraic identities. In this exercise, students learn how to recognise algebraic expressions that match standard identities and write them in their factorised form. Mastering this skill makes algebraic calculations faster, improves conceptual understanding, and builds a strong foundation for higher mathematics. These solutions follow the latest NCERT Ganita Manjari (2026) textbook and the CBSE Class 9 syllabus.
🎯 What You’ll Learn
Learn how to identify algebraic identities, recognise perfect square trinomials, factorise expressions using (a+b)² and (a−b)², and apply identities confidently to solve NCERT questions.
📝 Why This Exercise Matters
The concepts learned in this exercise form the foundation for factorisation, quadratic expressions, polynomial simplification, and many advanced algebra topics in higher classes. These questions are also important from the CBSE examination point of view.
📚 Important Concepts Covered
📑 Table of Contents
Quickly navigate to any section of Class 9 Maths Chapter 4 Exercise 4.2 Solutions using the links below.
📝 Question 1
Factorise the following expressions.
🧮 Question 2
Factorise each expression using suitable identities.
📚 More in This Page
Helpful learning resources available on this page.
⭐ Learn Before You Solve
Before going to Class 9 Maths Chapter 4 Exercise 4.2 Solutions , make sure you know how to recognise the correct algebraic identity. Once you identify the pattern correctly, factorising the expression becomes quick and easy.
🔍 Step 1
Observe the given expression carefully and identify whether it looks like a perfect square.
🧠 Step 2
Identify the first term (a²), last term (b²) and check whether the middle term is +2ab or −2ab.
✍ Step 3
Apply the correct identity. If every term has a common factor, take it out first and then use the identity.
📖 Algebraic Identities Used
Identity 1
(a + b)2 = a2 + 2ab + b2
Identity 2
(a − b)2 = a2 − 2ab + b2
💡 Remember
- Always identify a² and b² first.
- Check whether the middle term is +2ab or −2ab.
- If a common factor exists, factor it out before applying an identity.
- Verify your answer by expanding the factorised expression.
🎯 Exam Tip
In CBSE examinations, many students choose the wrong identity because they do not check the sign of the middle term carefully. Always compare the expression with the standard identities before factorising.
Identity 1
Identity 2
💡 Remember
- Always identify a² and b² first.
- Check whether the middle term is +2ab or −2ab.
- If a common factor exists, factor it out before applying an identity.
- Verify your answer by expanding the factorised expression.
🎯 Exam Tip
In CBSE examinations, many students choose the wrong identity because they do not check the sign of the middle term carefully. Always compare the expression with the standard identities before factorising.
📝 Class 9 Maths Chapter 4 Exercise 4.2 Solutions
Now that you have understood the concepts and algebraic identities, let’s solve each question of Class 9 Maths Chapter 4 Exercise 4.2 step by step. Every solution is prepared according to the latest NCERT Ganita Manjari (2026) textbook and follows the CBSE answer-writing format, making it easy to understand and perfect for homework, revision, and examinations.
Factor completely:
2ab = 24xy
b2 = 16y2
b = 4y
= (3x + 4y)2
2ab = 20st
b2 = 25t2
b = 5t
= (2s + 5t)2
2ab = 28xy
b2 = 4y2
b = 2y
= (7x + 2y)2
2ab = 32 3 pq
b2 = 4 9 q2
b = 2 3 q
= (8p + 2 3 q)2
2ab = 4ab
b2 = 4 3 b2
b = 2 √3 b
= (√3a + 2 √3 b)2
2ab = 6sv
b2 = 5v2
b = √5v
= ( 3 √5 s + √5v )2
∴ 792 = (80 − 1)2
= 802 − 2 × 80 × 1 + 12
= 6400 − 160 + 1
= 6241
∴ 1932 = (200 − 7)2
= 2002 − 2 × 200 × 7 + 72
= 40000 − 2800 + 49
= 37249
∴ 2992 = (300 − 1)2
= 3002 − 2 × 300 × 1 + 12
= 90000 − 600 + 1
= 89401
🚀 Quick Revision Dashboard
Revise the complete Class 9 Maths Chapter 4 Exercise 4.2 in just one minute with these important formulas, concepts, and exam tips.
📖 Important Formula
(a − b)2 = a2 − 2ab + b2
💡 Always Remember
- Identify a² and b² first.
- Check the sign of the middle term.
- Use the correct algebraic identity.
- Take common factor first, if required.
❌ Avoid These Mistakes
- Using the wrong identity.
- Ignoring the negative sign.
- Not taking the common factor.
- Skipping answer verification.
🎯 Exam Tip
First compare the expression with the standard identities. Once the pattern is recognised, factorisation becomes quick and accurate.
❓ Frequently Asked Questions
Find answers to the most common questions about Class 9 Maths Chapter 4 Exercise 4.2 Solutions and factorisation using algebraic identities.
1. What is the main concept of Exercise 4.2?
Exercise 4.2 focuses on factorising algebraic expressions using standard algebraic identities such as (a + b)2 and (a − b)2.
2. Which algebraic identities are used in Exercise 4.2?
The two main identities used are:
(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
3. How can I identify the correct identity?
First identify the first term (a2) and the last term (b2). Then check whether the middle term is +2ab or −2ab to choose the correct identity.
4. Are these solutions based on the latest NCERT textbook?
Yes. These solutions are prepared according to the latest NCERT Ganita Manjari (2026) textbook and follow the CBSE Class 9 syllabus.
5. Are these solutions useful for CBSE exams?
Yes. Every solution is explained step by step in a CBSE answer-writing format, making them useful for homework, revision, classroom learning, and examination preparation.
📚 Continue Learning
Continue your journey through Class 9 Maths Chapter 4 by navigating to the previous or next exercise, or explore solutions from other chapters.
🔗 Useful Resources
Explore these official educational resources for authentic CBSE and NCERT study materials.
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These Class 9 Maths Chapter 4 Exercise 4.2 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.
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