Class 9 Mathematics Chapter 4 Exploring Algebraic Identities – Extra Questions with Answers

Extra practice questions for Class 9 Maths Chapter 4 (Exploring Algebraic Identities), beyond the textbook. These Class 9 Mathematics Chapter 4 important questions are handy for last-minute exam practice.

Very Short Answer Questions (1 mark)

Q1. Expand (x + 5)² using the identity.
Ans: x² + 10x + 25.

Q2. Factorise x² − 16 using the difference of squares identity.
Ans: (x + 4)(x − 4).

Q3. Expand (a − 3)².
Ans: a² − 6a + 9.

Q4. State the identity used to expand (x + 2)(x + 5).
Ans: (x + a)(x + b) = x² + (a+b)x + ab.

Q5. Write the identity for a³ + b³ in factored form.
Ans: a³ + b³ = (a + b)(a² − ab + b²).

Short Answer Questions (2–3 marks)

Q6. Use a suitable identity to evaluate 998² without direct multiplication.
Ans: 998² = (1000 − 2)² = 1000² − 2×1000×2 + 2² = 1000000 − 4000 + 4 = 996004.

Q7. Factorise 4x² − 9y² using an identity, showing your working.
Ans: 4x² − 9y² = (2x)² − (3y)² = (2x + 3y)(2x − 3y), using the difference of squares identity.

Q8. Expand (2x + 3y)² using the standard identity, showing the substitution.
Ans: Using (a+b)² = a²+2ab+b² with a=2x, b=3y: (2x+3y)² = (2x)² + 2(2x)(3y) + (3y)² = 4x² + 12xy + 9y².

Higher-Order Thinking / Application Questions

Q9. If a + b = 10 and ab = 21, find the value of a² + b² without finding a and b individually.
Ans: Using (a+b)² = a² + 2ab + b²: 10² = a² + 2(21) + b², so 100 = a² + b² + 42, giving a² + b² = 58.

Q10. A square garden of side (x + 4) metres has a square flower bed of side x metres removed from one corner. Using algebraic identities, find a simplified expression for the remaining garden area.
Ans: Total area = (x+4)² = x² + 8x + 16 (using the identity). Flower bed area = x². Remaining area = (x² + 8x + 16) − x² = 8x + 16 = 8(x + 2) square metres.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.