Class 9 Maths Chapter 4 MCQs with Answers – Exploring Algebraic Identities

Class 9 Maths Chapter 4 MCQs

Question 1. Which of the following is the correct identity for (a + b)²?

A. a² + b²

B. a² + 2ab + b²

C. a² − 2ab + b²

D. a² − b²

Question 2. Expand (x − 3)².

A. x² − 9

B. x² + 6x + 9

C. x² − 6x + 9

D. x² − 3x + 9

Question 3. What is the value of (a + b)(a − b)?

A. a² + 2ab + b²

B. a² − b²

C. a² + b²

D. a² − 2ab + b²

Question 4. Expand (x + 5)².

A. x² + 10x + 25

B. x² + 5x + 25

C. x² − 10x + 25

D. x² + 25

Question 5. Which expression is equal to (a − b)²?

A. a² − b²

B. a² + 2ab + b²

C. a² − 2ab + b²

D. a² + b²

Question 6. Simplify (x + 2)(x + 3).

A. x² + 5x + 6

B. x² + 6x + 5

C. x² + x + 6

D. x² + 5

Question 7. What is the expansion of (2x + 1)²?

A. 4x² + 1

B. 4x² + 2x + 1

C. 4x² + 4x + 1

D. 2x² + 4x + 1

Question 8. Simplify (3a − 2b)².

A. 9a² − 4b²

B. 9a² − 12ab + 4b²

C. 9a² + 12ab + 4b²

D. 3a² − 12ab + 2b²

Question 9. Which expression is equal to x² − 16?

A. (x − 4)²

B. (x + 4)²

C. (x − 4)(x + 4)

D. (x − 8)(x + 2)

Question 10. Find the value of (a + 4)(a − 4).

A. a² + 16

B. a² − 8a + 16

C. a² + 8a + 16

D. a² − 16

Question 11. If x + y = 10 and xy = 21, find x² + y².

A. 58

B. 100

C. 79

D. 42

Question 12. If a − b = 5 and ab = 6, find a² + b².

A. 13

B. 25

C. 37

D. 31

Question 13. Factorise x² + 7x + 12.

A. (x + 2)(x + 6)

B. (x + 3)(x + 4)

C. (x − 3)(x − 4)

D. (x + 1)(x + 12)

Question 14. What is the value of (101)² using an algebraic identity?

A. 10,101

B. 10,201

C. 10,001

D. 10,2010

Question 15. Simplify (x + y)² − (x − y)².

A. 2x² + 2y²

B. x² − y²

C. 4xy

D. 2xy

Answer Key – Class 9 Maths Chapter 4 MCQs

1. Question 1 — Correct Answer: B. a² + 2ab + b² Identity: (a + b)² = a² + 2ab + b².
2. Question 2 — Correct Answer: C. x² − 6x + 9 (x − 3)² = x² − 2(x)(3) + 3² = x² − 6x + 9.
3. Question 3 — Correct Answer: B. a² − b² Identity: (a + b)(a − b) = a² − b².
4. Question 4 — Correct Answer: A. x² + 10x + 25 (x + 5)² = x² + 2(x)(5) + 25 = x² + 10x + 25.
5. Question 5 — Correct Answer: C. a² − 2ab + b² Identity: (a − b)² = a² − 2ab + b².
6. Question 6 — Correct Answer: A. x² + 5x + 6 (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.
7. Question 7 — Correct Answer: C. 4x² + 4x + 1 (2x + 1)² = (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1.
8. Question 8 — Correct Answer: B. 9a² − 12ab + 4b² (3a − 2b)² = (3a)² − 2(3a)(2b) + (2b)² = 9a² − 12ab + 4b².
9. Question 9 — Correct Answer: C. (x − 4)(x + 4) Using a² − b² = (a − b)(a + b), x² − 16 = x² − 4² = (x − 4)(x + 4).
10. Question 10 — Correct Answer: D. a² − 16 (a + 4)(a − 4) = a² − 4² = a² − 16.
11. Question 11 — Correct Answer: A. 58 x² + y² = (x + y)² − 2xy = 10² − 2(21) = 100 − 42 = 58.
12. Question 12 — Correct Answer: C. 13 (a − b)² = a² − 2ab + b². Therefore, a² + b² = (a − b)² + 2ab = 5² + 2(6) = 25 + 12 = 37.
13. Question 13 — Correct Answer: B. (x + 3)(x + 4) The numbers 3 and 4 add to 7 and multiply to 12. Therefore, x² + 7x + 12 = (x + 3)(x + 4).
14. Question 14 — Correct Answer: B. 10,201 101² = (100 + 1)² = 100² + 2(100)(1) + 1² = 10,000 + 200 + 1 = 10,201.
15. Question 15 — Correct Answer: C. 4xy (x + y)² − (x − y)² = (x² + 2xy + y²) − (x² − 2xy + y²) = 4xy.

Want More Practice?

Take your algebra skills to the next level with our Class 9 Maths Chapter 4 Worksheet — 50 MCQs from Science World By Tushar Sir.

Class 9 Maths · Chapter 4

• Practise additional chapter-wise questions.
• Revise important algebraic identities.
• Check your answers using the answer key.
• Download the worksheet PDF for convenient practice.