{"id":4573,"date":"2026-06-15T16:53:53","date_gmt":"2026-06-15T11:23:53","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=4573"},"modified":"2026-06-15T16:53:57","modified_gmt":"2026-06-15T11:23:57","slug":"ncert-class-9-maths-exercise-4-3-solutions-more-algebraic-identities","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-4-3-solutions-more-algebraic-identities\/","title":{"rendered":"NCERT Class 9 Maths Exercise 4.3 Solutions \u2013 More Algebraic Identities"},"content":{"rendered":"
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Short Introduction<\/h1>\n\n\n\n

Exercise 4.3 introduces advanced algebraic identities and their applications in squaring numbers, factorisation, expansion of expressions, and proving identities. These identities simplify lengthy calculations and strengthen algebraic thinking.<\/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>4.3<\/td><\/tr>
Class<\/td>9<\/td><\/tr>
Main Topic<\/td>More Algebraic Identities<\/td><\/tr>
Difficulty Level<\/td>Moderate<\/td><\/tr>
Skills Developed<\/td>Expansion, Factorisation, Proof of Identities<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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Concepts Used (Topics Covered)<\/h1>\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

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

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

✅ Numerical Squaring<\/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>

✅ Identity Verification<\/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

Identity 3<\/h2>\n\n\n\n

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

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

Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier.<\/strong><\/p>\n\n\n\n

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(i) 117²<\/h2>\n\n\n\n
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(ii) 78²<\/h2>\n\n\n\n
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(iii) 198²<\/h2>\n\n\n\n
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(iv) 214²<\/h2>\n\n\n\n
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(v) 1104²<\/h2>\n\n\n\n
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(vi) 1120²<\/h2>\n\n\n\n
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Question 2<\/h1>\n\n\n\n

Factor Using Suitable Identities<\/p>\n\n\n\n

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(i) 16y² − 24y + 9<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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(ii) (9\/4)s² + 6st + 4t²<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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(iii)<\/h2>\n\n\n\n
Related Topic to Read more<\/span>Class 9 Maths Exercise 1.2 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div>

m²\/9 + mk\/3 + k²\/4 + 3nk + 2mn + 9n²<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
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(iv)<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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(v)<\/h2>\n\n\n\n

9a² + 4b² + c² −12ab +6ac −4bc<\/p>\n\n\n\n

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

Expand the following using the identity<\/p>

\"\"<\/a><\/div><\/div>\n\n\n\n

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

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(i) (p + 3q + 7r)²<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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(ii) (3x − 2y + 4z)²<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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Question 4<\/h1>\n\n\n\n

Is this an Identity?<\/p>\n\n\n\n

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

\"\"<\/figure>\n\n\n\n
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Final Answers Summary<\/h1>\n\n\n\n

Question 1<\/h2>\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>

(i) 13689<\/p>\n\n\n\n

(ii) 6084<\/p>\n\n\n\n

(iii) 39204<\/p>\n\n\n\n

(iv) 45796<\/p>\n\n\n\n

(v) 1218816<\/p>\n\n\n\n

(vi) 1254400<\/p>\n\n\n\n

Question 2<\/h2>\n\n\n\n

(i) (4y−3)²<\/p>\n\n\n\n

(ii) (3s\/2+2t)²<\/p>\n\n\n\n

(iii) (m\/3+k\/2+3n)²<\/p>\n\n\n\n

(iv) (p\/4−4\/p)²<\/p>\n\n\n\n

(v) (3a−2b+c)²<\/p>\n\n\n\n

Question 3<\/h2>\n\n\n\n

(i) p²+9q²+49r²+6pq+14pr+42qr<\/p>\n\n\n\n

(ii) 9x²+4y²+16z²−12xy+24xz−16yz<\/p>\n\n\n\n

Question 4<\/h2>\n\n\n\n

Not an Identity<\/p>\n\n\n\n

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

❌ Forgetting cross-product terms in (a+b+c)².<\/p>\n\n\n\n

❌ Wrong sign while expanding negative terms.<\/p>\n\n\n\n

❌ Ignoring coefficients during factorisation.<\/p>\n\n\n\n

❌ Confusing equation with identity.<\/p>\n\n\n\n

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

⭐ Identify the most suitable identity before solving.<\/p>\n\n\n\n

⭐ Write identity first to gain step marks.<\/p>\n\n\n\n

⭐ Check signs carefully in (a−b)².<\/p>\n\n\n\n

⭐ Verify factorisation by re-expanding.<\/p>\n\n\n\n

⭐ For numerical squares, choose nearest multiples of 10, 100, or 1000.<\/p>\n\n\n\n

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

1. (a+b+c)² contains how many cross-product terms?<\/h3>\n\n\n\n

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

B. 3<\/p>\n\n\n\n

C. 4<\/p>\n\n\n\n

D. 6<\/p>\n\n\n\n

✅ Answer: B<\/p>\n\n\n\n

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2. 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: C<\/p>\n\n\n\n

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3. 98² equals<\/h3>\n\n\n\n

A. 9604<\/p>\n\n\n\n

B. 9804<\/p>\n\n\n\n

C. 9504<\/p>\n\n\n\n

D. 9904<\/p>\n\n\n\n

✅ Answer: A<\/p>\n\n\n\n

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4. Which identity is used for 199²?<\/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: B<\/p>\n\n\n\n

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

Q1. When should we use (a+b+c)²?<\/h3>\n\n\n\n

When an expression contains three terms whose square is required.<\/p>\n\n\n\n

Q2. What is an identity?<\/h3>\n\n\n\n

An equation true for all values of variables.<\/p>\n\n\n\n

Q3. How is identity different from an equation?<\/h3>\n\n\n\n

An equation is true only for specific values, while an identity is true for all values.<\/p>\n\n\n\n

Q4. Why is factorisation important?<\/h3>\n\n\n\n

It simplifies algebraic expressions and helps solve equations quickly.<\/p>\n\n\n\n

Q5. Can identities help in mental calculations?<\/h3>\n\n\n\n

Yes. They are widely used for quick squaring and simplification.<\/p>\n\n\n\n

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