Class 9 Maths Chapter 4 Exploring Algebraic Identities Worksheet

The Chapter 4 Exploring Algebraic Identities worksheet with answers is designed for Class 9 students to practice important algebra concepts through different types of questions. This worksheet includes identity-based problems, expansion questions, factorisation practice, numerical calculations, and step-by-step answers to help students understand algebraic identities clearly.

These Worksheets follow the latest NCERT Class 9 Maths learning approach and help students apply formulas instead of only memorising them. Students searching for Class 9 Worksheets can use this chapter-wise practice material for homework, revision, and exam preparation.

The Class 9 Maths Worksheets provide structured questions with solutions to improve accuracy and problem-solving skills. By solving this worksheet, students will learn how algebraic identities are used to simplify expressions, calculate values quickly, and solve different types of mathematical problems.

What is Included in Exploring Algebraic Identities Worksheet?

The Chapter 4 Exploring Algebraic Identities worksheet PDF contains different levels of questions that help students build a strong understanding of algebraic formulas and their applications.

Learning Outcomes of Exploring Algebraic Identities Worksheet

After completing this Class 9 algebraic identities worksheet, students will be able to:

• Understand different algebraic identities and their uses.
• Expand algebraic expressions using formulas.
• Apply identities for faster calculations.
• Factorise expressions using suitable identities.
• Solve questions based on squares and cubes.
• Find values using algebraic relationships.
• Improve accuracy in algebra problems.

Exploring Algebraic Identities Worksheet Questions

Solve these Chapter 4 Exploring Algebraic Identities worksheet questions to practice formulas, calculations, and application-based problems.

Section A: Concept Practice

1. Write the expansion of the following algebraic identities:

a) (a + b)²

b) (a - b)²

c) (a + b)(a - b)

2. Expand the following expression using a suitable identity:

(5x + 3y)²

3. Simplify using algebraic identity:

(8a - 4b)²

4. Expand:

(x + 2y + 3z)²

5. Identify the algebraic identity used in:

25x² - 16y²

Section B: Application Practice

6. Evaluate using algebraic identities:

a) (102)²

b) (98)²

7. Find the value without direct multiplication:

53 × 47

8. Factorise the expression using identities:

9x² + 30x + 25

9. Factorise:

36a² - 49b²

10. Simplify using suitable identity:

(x + 4)(x + 7)

Section C: Exam Practice Questions

11. If x + 1/x = 5, find the value of:

x² + 1/x²

12. If a + b = 8 and ab = 15, find:

a² + b²

13. Evaluate without calculating cubes directly:

(-10)³ + (6)³ + (4)³

Exploring Algebraic Identities Answers

Check the Chapter 4 Exploring Algebraic Identities worksheet answer key below with detailed solutions.

Section A Answers

1. Answer:

a) (a + b)² = a² + 2ab + b²

b) (a - b)² = a² - 2ab + b²

c) (a + b)(a - b) = a² - b²

Explanation:

These are standard algebraic identities used for expanding and simplifying expressions.

2. Answer:

Given:

(5x + 3y)²

Using:

(a+b)² = a² + 2ab + b²

= (5x)² + 2(5x)(3y) + (3y)²

= 25x² + 30xy + 9y²

3. Answer:

(8a - 4b)²

Using:

(a-b)² = a² - 2ab + b²

= (8a)² - 2(8a)(4b) + (4b)²

= 64a² - 64ab + 16b²

4. Answer:

(x + 2y + 3z)²

Using:

(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

= x² + 4y² + 9z² + 4xy + 12yz + 6xz

5. Answer:

25x² - 16y²

= (5x)² - (4y)²

Identity used:

a² - b² = (a+b)(a-b)

Section B Answers

6. Answers:

a) (102)²

= (100 + 2)²

= 10000 + 400 + 4

= 10404

b) (98)²

= (100 - 2)²

= 10000 - 400 + 4

= 9604

7. Answer:

53 × 47

= (50+3)(50-3)

Using:

(a+b)(a-b)=a²-b²

= 50² - 3²

= 2500 - 9

= 2491

8. Answer:

9x² + 30x + 25

= (3x)² + 2(3x)(5) + 5²

= (3x + 5)²

9. Answer:

36a² - 49b²

= (6a)² - (7b)²

= (6a+7b)(6a-7b)

10. Answer:

(x + 4)(x + 7)

Using:

(x+a)(x+b)=x²+(a+b)x+ab

= x² + (4+7)x + (4×7)

= x² + 11x + 28

Section C Answers

11. Answer:

Given:

x + 1/x = 5

Squaring both sides:

(x + 1/x)² = 25

x² + 1/x² + 2 = 25

x² + 1/x² = 25 - 2

= 23

12. Answer:

Given:

a + b = 8
ab = 15

Using:

(a+b)² = a²+b²+2ab

64 = a²+b²+30

a²+b² = 64-30

= 34

13. Answer:

Given:

(-10)³ + 6³ + 4³

Here,

-10 + 6 + 4 = 0

Using:

If a+b+c=0,

a³+b³+c³ = 3abc

= 3(-10)(6)(4)

= -720

Important Concepts Practiced

This worksheet on questions based on algebraic identities for Class 9 with solutions covers:

• Algebraic identity formulas
• Expansion of algebraic expressions
• Square identities
• Difference of squares identity
• Three-term identity
• Cube identities
• Factorisation using identities
• Simplification of expressions
• Value-based algebra problems
• Faster calculations using identities

Key Takeaways from Exploring Algebraic Identities

• Algebraic identities are formulas that are true for all values of variables.
• Identities help students simplify large expressions easily.
• Square and cube identities reduce calculation time.
• Factorisation becomes easier by recognising identity patterns.
• Regular worksheet practice improves algebra skills and exam preparation.