{"id":4585,"date":"2026-06-15T18:02:00","date_gmt":"2026-06-15T12:32:00","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=4585"},"modified":"2026-06-15T18:02:04","modified_gmt":"2026-06-15T12:32:04","slug":"ncert-class-9-maths-exercise-4-4-solutions-algebraic-identities","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-4-4-solutions-algebraic-identities\/","title":{"rendered":"NCERT Class 9 Maths Exercise 4.4 Solutions \u2013 Algebraic Identities"},"content":{"rendered":"
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Short Introduction<\/h1>\n\n\n\n

Exercise 4.4 focuses on factorisation using algebraic identities and quick numerical calculations using identities. Students learn how to split middle terms, identify suitable identities, and factor quadratic expressions efficiently. These concepts form the foundation for higher algebra and competitive examinations.<\/p>\n\n\n\n

This complete solution guide by www.mymockmate.com<\/a><\/strong> provides detailed step-by-step explanations for every question in Exercise 4.4.<\/p>\n\n\n\n

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Quick Information Box<\/h1>\n\n\n\n
Particular<\/th>Details<\/th><\/tr><\/thead>
Class<\/td>9<\/td><\/tr>
Subject<\/td>Mathematics<\/td><\/tr>
Chapter<\/td>Exploring Algebraic Identities<\/td><\/tr>
Exercise<\/td>4.4<\/td><\/tr>
Topic<\/td>Factorisation and Applications of Identities<\/td><\/tr>
Difficulty Level<\/td>Medium<\/td><\/tr>
Exam Importance<\/td>High<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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Concepts Used (Topics Covered)<\/h1>\n\n\n\n

✓ Factorisation of Quadratic Expressions<\/p>\n\n\n\n

✓ Splitting the Middle Term<\/p>\n\n\n\n

✓ Difference of Squares Identity<\/p>\n\n\n\n

✓ Perfect Square 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>

✓ Numerical Calculations Using Identities<\/p>\n\n\n\n

✓ Product of Numbers Near a Base Number<\/p>\n\n\n\n

✓ Algebraic Manipulation<\/p>\n\n\n\n

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

1. Square of Sum<\/h3>\n\n\n\n

(a + b)² = a² + 2ab + b²<\/p>\n\n\n\n

2. Square of Difference<\/h3>\n\n\n\n

(a − b)² = a² − 2ab + b²<\/p>\n\n\n\n

3. Difference of Squares<\/h3>\n\n\n\n

a² − b² = (a + b)(a − b)<\/p>\n\n\n\n

4. Three Variable Identity<\/h3>\n\n\n\n
Related Topic to Read more<\/span>Class 9 Maths Exercise 1.2 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div>

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca<\/p>\n\n\n\n

5. Factorisation Form<\/h3>\n\n\n\n

x² + (a+b)x + ab = (x+a)(x+b)<\/p>\n\n\n\n

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

Fill in the blanks to complete the following identities.<\/p>

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

Select and use the identity that will help you to find the following products without multiplying directly:<\/strong><\/p>\n\n\n\n

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Question 3<\/h1>\n\n\n\n

Factor the following.<\/p>\n\n\n\n

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(i)<\/h2>\n\n\n\n

9a² + b² +4c² −6ab +12ac −4bc<\/p>\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>

(3a − b + 2c)²<\/p>\n\n\n\n

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(ii)<\/h2>\n\n\n\n

16s² +25t² −40st<\/p>\n\n\n\n

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

(4s−5t)²<\/p>\n\n\n\n

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(iii)<\/h2>\n\n\n\n

r² − r −42<\/p>\n\n\n\n

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

(r−7)(r+6)<\/p>\n\n\n\n

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(iv)<\/h2>\n\n\n\n

49g² +14gh +h²<\/p>\n\n\n\n

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

(7g+h)²<\/p>\n\n\n\n

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(v)<\/h2>\n\n\n\n

64u² +121v² +4w² −176uv −32uw +44vw<\/p>\n\n\n\n

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

(8u −11v −2w)²<\/p>\n\n\n\n

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

❌ Choosing incorrect numbers while splitting the middle term.<\/p>\n\n\n\n

❌ Ignoring negative signs.<\/p>\n\n\n\n

❌ Confusing (a+b)² and a²+b².<\/p>\n\n\n\n

❌ Errors while identifying perfect square trinomials.<\/p>\n\n\n\n

❌ Forgetting verification after factorisation.<\/p>\n\n\n\n

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

✅ Always check Sum and Product conditions.<\/p>\n\n\n\n

✅ Memorise all standard identities.<\/p>\n\n\n\n

✅ Verify factorisation by multiplying factors.<\/p>\n\n\n\n

✅ Use identities for fast calculations.<\/p>\n\n\n\n

✅ Practice factorisation daily.<\/p>\n\n\n\n

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

1. Factor x²−9<\/h3>\n\n\n\n

A. (x−3)²<\/p>\n\n\n\n

B. (x+3)²<\/p>\n\n\n\n

C. (x+3)(x−3)<\/p>\n\n\n\n

D. None<\/p>\n\n\n\n

Answer: C<\/p>\n\n\n\n

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2. 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. 9601<\/p>\n\n\n\n

Answer: A<\/p>\n\n\n\n

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3. Factor x²+9x+20<\/h3>\n\n\n\n

A. (x+4)(x+5)<\/p>\n\n\n\n

B. (x+2)(x+10)<\/p>\n\n\n\n

C. (x+1)(x+20)<\/p>\n\n\n\n

D. None<\/p>\n\n\n\n

Answer: A<\/p>\n\n\n\n

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4. Which identity is used in 23×17?<\/h3>\n\n\n\n

A. (a+b)²<\/p>\n\n\n\n

B. (a−b)²<\/p>\n\n\n\n

C. a²−b²<\/p>\n\n\n\n

D. None<\/p>\n\n\n\n

Answer: C<\/p>\n\n\n\n

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5. Factor 25x²−30x+9<\/h3>\n\n\n\n

A. (5x−3)²<\/p>\n\n\n\n

B. (5x+3)²<\/p>\n\n\n\n

C. (25x−9)<\/p>\n\n\n\n

D. None<\/p>\n\n\n\n

Answer: A<\/p>\n\n\n\n

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

Q1. What is the main topic of Exercise 4.4?<\/h3>\n\n\n\n

Factorisation and application of algebraic identities.<\/p>\n\n\n\n

Q2. How do we factor x² + bx + c?<\/h3>\n\n\n\n

Find two numbers whose sum is b and product is c.<\/p>\n\n\n\n

Q3. Why are identities useful?<\/h3>\n\n\n\n

They simplify calculations and factorisation.<\/p>\n\n\n\n

Q4. Can identities be used in competitive exams?<\/h3>\n\n\n\n

Yes. They save time and improve accuracy.<\/p>\n\n\n\n

Q5. Which identity is most important here?<\/h3>\n\n\n\n

a²−b²=(a+b)(a−b)<\/p>\n\n\n\n

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🚀 Looking for more NCERT Solutions, Chapter-wise Notes, Mock Tests, Previous Year Questions, Practice Worksheets and Exam Preparation Resources?<\/p>\n\n\n\n

Visit:<\/p>\n\n\n\n

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

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