{"id":4563,"date":"2026-06-15T16:12:44","date_gmt":"2026-06-15T10:42:44","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=4563"},"modified":"2026-06-15T16:12:48","modified_gmt":"2026-06-15T10:42:48","slug":"ncert-class-9-maths-exercise-4-2-solutions-factorisation-using-algebraic-identities","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-4-2-solutions-factorisation-using-algebraic-identities\/","title":{"rendered":"NCERT Class 9 Maths Exercise 4.2 Solutions \u2013 Factorisation Using Algebraic Identities"},"content":{"rendered":"
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Short Introduction<\/h1>\n\n\n\n

Exercise 4.2 focuses on factorisation using algebraic identities. Students learn how to recognize perfect square trinomials and convert them into factors using the identities:<\/p>\n\n\n\n

(a + b)² = a² + 2ab + b²<\/p>\n\n\n\n

(a − b)² = a² − 2ab + b²<\/p>\n\n\n\n

These techniques simplify algebraic expressions and help solve mathematical problems quickly.<\/p>\n\n\n\n

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Quick Information Box<\/h1>\n\n\n\n
Particular<\/th>Details<\/th><\/tr><\/thead>
Chapter<\/td>Exploring Algebraic Identities<\/td><\/tr>
Exercise<\/td>4.2<\/td><\/tr>
Topic<\/td>Factorisation Using Identities<\/td><\/tr>
Class<\/td>9<\/td><\/tr>
Difficulty Level<\/td>Moderate<\/td><\/tr>
Main Identities<\/td>(a+b)² and (a−b)²<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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Concepts Used (Topics Covered)<\/h1>\n\n\n\n

✅ Perfect Square Trinomials<\/p>\n\n\n\n

✅ Factorisation by Identities<\/p>\n\n\n\n

Related Topic to Read more<\/span>Class 9 Maths Exercise 1.1 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div>

✅ Common Factor Method<\/p>\n\n\n\n

✅ Expansion Verification<\/p>\n\n\n\n

✅ Numerical Calculation using (a−b)²<\/p>\n\n\n\n

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Important Formulas<\/h1>\n\n\n\n

Identity 1<\/h2>\n\n\n\n

(a + b)² = a² + 2ab + b²<\/p>\n\n\n\n

Identity 2<\/h2>\n\n\n\n

(a − b)² = a² − 2ab + b²<\/p>\n\n\n\n

Factorisation Forms<\/h2>\n\n\n\n

a² + 2ab + b² = (a + b)²<\/p>\n\n\n\n

Related Topic to Read more<\/span>Class 9 Maths Exercise 1.2 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div>

a² − 2ab + b² = (a − b)²<\/p>\n\n\n\n

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Question 1<\/h1>\n\n\n\n

Factor Completely<\/p>\n\n\n\n

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(i) 9x² + 24xy + 16y²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Answer<\/h3>\n\n\n\n

(3x + 4y)²<\/p>

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(ii) 4s² + 20st + 25t²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Answer<\/h3>\n\n\n\n

(2s + 5t)²<\/p>\n\n\n\n

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(iii) 49x² + 28xy + 4y²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Answer<\/h3>\n\n\n\n

(7x + 2y)²<\/p>\n\n\n\n

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(iv) 64p² + (32\/3)pq + (4\/9)q²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Answer<\/h3>\n\n\n\n

(8p + 2q\/3)²<\/p>\n\n\n\n

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(v) 3a² + 4ab + (4\/3)b²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Answer<\/h3>\n\n\n\n
Related Topic to Read more<\/span>Class 9 Maths End of Chapter Exercise Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div>

(1\/3)(3a + 2b)²<\/p>\n\n\n\n

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(vi) (9\/5)s² + 6sv + 5v²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Answer<\/h3>\n\n\n\n

(1\/5)(3s + 5v)²<\/p>\n\n\n\n

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Question 2<\/h1>\n\n\n\n

Find the values of the following using the identity<\/p>\n\n\n\n

(a − b)² = a² − 2ab + b²<\/p>\n\n\n\n

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(i) (79)²<\/h2>\n\n\n\n
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(ii) (193)²<\/h2>\n\n\n\n
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(iii) (299)²<\/h2>\n\n\n\n

Solution<\/h3>\n\n\n\n
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Final Answers Summary<\/h1>\n\n\n\n

Question 1<\/h3>\n\n\n\n

(i) (3x + 4y)²<\/p>\n\n\n\n

(ii) (2s + 5t)²<\/p>\n\n\n\n

(iii) (7x + 2y)²<\/p>\n\n\n\n

(iv) (8p + 2q\/3)²<\/p>\n\n\n\n

(v) (1\/3)(3a + 2b)²<\/p>\n\n\n\n

(vi) (1\/5)(3s + 5v)²<\/p>\n\n\n\n

Question 2<\/h3>\n\n\n\n

(i) 6241<\/p>\n\n\n\n

(ii) 37249<\/p>\n\n\n\n

(iii) 89401<\/p>\n\n\n\n

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Common Mistakes<\/h1>\n\n\n\n

❌ Ignoring the middle term while checking identities.<\/p>\n\n\n\n

❌ Forgetting to take common factors in Questions (v) and (vi).<\/p>\n\n\n\n

❌ Wrong square of fractions.<\/p>\n\n\n\n

❌ Incorrect calculation of 2ab.<\/p>\n\n\n\n

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Exam Tips<\/h1>\n\n\n\n

⭐ First identify the first square term.<\/p>\n\n\n\n

⭐ Check whether the last term is also a perfect square.<\/p>\n\n\n\n

⭐ Verify the middle term equals 2ab.<\/p>\n\n\n\n

⭐ Always factor out common factors first.<\/p>\n\n\n\n

⭐ Use identities for quick calculations of numbers near 100, 200 or 300.<\/p>\n\n\n\n

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Practice MCQs<\/h1>\n\n\n\n

1. Factorise x² + 10x + 25<\/h3>\n\n\n\n

A. (x+5)<\/p>\n\n\n\n

B. (x+5)²<\/p>\n\n\n\n

C. (x−5)²<\/p>\n\n\n\n

D. x(x+25)<\/p>\n\n\n\n

✅ Answer: B<\/p>\n\n\n\n

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2. Factorise 4a² +12ab +9b²<\/h3>\n\n\n\n

A. (2a+3b)<\/p>\n\n\n\n

B. (2a+3b)²<\/p>\n\n\n\n

C. (2a−3b)²<\/p>\n\n\n\n

D. (4a+9b)<\/p>\n\n\n\n

✅ Answer: B<\/p>\n\n\n\n

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3. 99² equals<\/h3>\n\n\n\n

A. 9801<\/p>\n\n\n\n

B. 9901<\/p>\n\n\n\n

C. 9701<\/p>\n\n\n\n

D. 9999<\/p>\n\n\n\n

✅ Answer: A<\/p>\n\n\n\n

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4. Which identity is used for (a−b)²?<\/h3>\n\n\n\n

A. a²+2ab+b²<\/p>\n\n\n\n

B. a²−2ab+b²<\/p>\n\n\n\n

C. a²−b²<\/p>\n\n\n\n

D. (a+b)(a−b)<\/p>\n\n\n\n

✅ Answer: B<\/p>\n\n\n\n

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FAQ Section<\/h1>\n\n\n\n

Q1. What is a perfect square trinomial?<\/h3>\n\n\n\n

An expression of the form:<\/p>\n\n\n\n

a² + 2ab + b²<\/p>\n\n\n\n

or<\/p>\n\n\n\n

a² − 2ab + b²<\/p>\n\n\n\n

is called a perfect square trinomial.<\/p>\n\n\n\n

Q2. Why do we verify the middle term?<\/h3>\n\n\n\n

Because it must exactly equal 2ab.<\/p>\n\n\n\n

Q3. Why was common factor taken in Question (v)?<\/h3>\n\n\n\n

Without taking the common factor, the expression does not directly match an identity.<\/p>\n\n\n\n

Q4. Which identity is used for numerical squares?<\/h3>\n\n\n\n

(a−b)² = a² −2ab + b²<\/p>\n\n\n\n

Q5. Is factorisation the reverse of expansion?<\/h3>\n\n\n\n

Yes. Expansion converts factors into expressions, while factorisation converts expressions into factors.<\/p>\n\n\n\n

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📚 Looking for complete Class 9 Maths solutions?<\/p>\n\n\n\n

Get chapter-wise NCERT solutions, mock tests, MCQs, previous year questions and detailed explanations at:<\/p>\n\n\n\n

👉 www.mymockmate.com<\/a><\/p>\n\n\n\n

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