Exploring Algebraic Identities — Class 9 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Exploring Algebraic Identities" — 10 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Exploring Algebraic Identities" — 10 important questions with detailed answers for…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 19, 2026

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Key Questions Covered:

Expand (3x + 4y)² using a suitable algebraic identity.
Factorize 25x² - 49y² using a suitable algebraic identity.
Multiply (p + 3)(p + 8) using a suitable algebraic identity.
Evaluate 103 × 97 using a suitable algebraic identity.
Expand (2x + y - 3z)² using a suitable algebraic identity.
Expand (2m - 3n)³ using a suitable algebraic identity.
+ 4 more questions in the full chapter

Solutions Summary:

Question	Status
Expand (3x + 4y)² using a suitable algebraic identity.	✓ Solved
Factorize 25x² - 49y² using a suitable algebraic identity.	✓ Solved
Multiply (p + 3)(p + 8) using a suitable algebraic identity.	✓ Solved
Evaluate 103 × 97 using a suitable algebraic identity.	✓ Solved
Expand (2x + y - 3z)² using a suitable algebraic identity.	✓ Solved
Expand (2m - 3n)³ using a suitable algebraic identity.	✓ Solved

Showing 6 of 10 questions

Q1: Expand (3x + 4y)² using a suitable algebraic identity.

Here, we will use the identity: (a + b)² = a² + 2ab + b² In our expression, (3x + 4y)²: Let a = 3x And b = 4y Now, substitute the values of a and b into the identity: (3x + 4y)² = (3x)² + 2(3x)(4y) + (4y)² First term: (3x)² = 3² × x² = 9x² Second term: 2(3x)(4y) = 2 × 3 × 4 × x × y = 24xy Third term: (4y)² = 4² × y² = 16y² So, (3x + 4y)² = 9x² + 24xy + 16y² This is the expanded form.

Q2: Factorize 25x² - 49y² using a suitable algebraic identity.

We need to factorize 25x² - 49y². This expression is in the form a² - b². We know the identity: a² - b² = (a - b)(a + b) First, we write 25x² as a square: 25x² = (5x)² Next, we write 49y² as a square: 49y² = (7y)² So, our expression becomes (5x)² - (7y)². Comparing this with a² - b², we have: a = 5x b = 7y Now, apply the identity (a - b)(a + b): (5x)² - (7y)² = (5x - 7y)(5x + 7y) Therefore, the factorized form of 25x² - 49y² is (5x - 7y)(5x + 7y).

Q3: Multiply (p + 3)(p + 8) using a suitable algebraic identity.

We need to multiply (p + 3)(p + 8). This expression is in the form (x + a)(x + b). We know the identity: (x + a)(x + b) = x² + (a + b)x + ab In our expression, (p + 3)(p + 8): Let x = p Let a = 3 Let b = 8 Now, substitute these values into the identity: (p + 3)(p + 8) = p² + (3 + 8)p + (3)(8) Calculate the terms: First term: p² Second term: (3 + 8)p = 11p Third term: (3)(8) = 24 So, (p + 3)(p + 8) = p² + 11p + 24 This is the product.

Q4: Evaluate 103 × 97 using a suitable algebraic identity.

We need to evaluate 103 × 97. We can write 103 as (100 + 3) and 97 as (100 - 3). So, the expression becomes (100 + 3)(100 - 3). This expression is in the form (a + b)(a - b). We know the identity: (a + b)(a - b) = a² - b² In our expression, (100 + 3)(100 - 3): Let a = 100 Let b = 3 Now, substitute these values into the identity: (100 + 3)(100 - 3) = 100² - 3² Calculate the terms: 100² = 100 × 100 = 10000 3² = 3 × 3 = 9 Now subtract: 10000 - 9 = 9991 Therefore, 103 × 97 = 9991.

Q5: Expand (2x + y - 3z)² using a suitable algebraic identity.

We need to expand (2x + y - 3z)². This expression is in the form (a + b + c)². We know the identity: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca In our expression, (2x + y - 3z)²: Let a = 2x Let b = y Let c = -3z (Note the negative sign is part of c) Now, substitute these values into the identity: (2x + y - 3z)² = (2x)² + (y)² + (-3z)² + 2(2x)(y) + 2(y)(-3z) + 2(-3z)(2x) Calculate each term: 1. (2x)² = 4x² 2. (y)² = y² 3. (-3z)² = (-3)² × z² = 9z² 4. 2(2x)(y) = 4xy 5. 2(y)(-3z) = -6yz 6. 2(-3z...

Q6: Expand (2m - 3n)³ using a suitable algebraic identity.

We need to expand (2m - 3n)³. This expression is in the form (a - b)³. We know the identity: (a - b)³ = a³ - 3a²b + 3ab² - b³ In our expression, (2m - 3n)³: Let a = 2m Let b = 3n Now, substitute these values into the identity: (2m - 3n)³ = (2m)³ - 3(2m)²(3n) + 3(2m)(3n)² - (3n)³ Calculate each term: 1. (2m)³ = 2³ × m³ = 8m³ 2. 3(2m)²(3n) = 3(4m²)(3n) = 3 × 4 × 3 × m² × n = 36m²n 3. 3(2m)(3n)² = 3(2m)(9n²) = 3 × 2 × 9 × m × n² = 54mn² 4. (3n)³ = 3³ × n³ = 27n³ Combine all the terms: (2m - 3n)³ = ...

Showing 6 of 10 questions. Visit the full page for complete solutions.