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Class 9 Maths: Exploring Algebraic Identities, 8 practice questions with answers
These are 8 practice questions on Chapter 4, Exploring Algebraic Identities, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). Each has a worked answer and the textbook page it comes from. They cover squaring numbers quickly with (a + b)² and (a − b)², multiplying two numbers with a² − b², expanding a square, factorising with identities, finding x² + y² from x + y and xy, and the cube identity (a + b)³. Try each one on paper before you open the answer. Powers come up again here, and the laws of exponents have their own set: Class 8 Power Play (Exponents) questions.
These questions are our own, drafted with AI help. Every number was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Facts from the NCERT textbook (Ganita Manjari: Mathematics, Textbook for Grade 9, Part I, Chapter 4, printed pages 68 to 91):
- An algebraic identity is an equation that is true for all values of the variables in it; an equation need not be true for all values (page 70).
- (a + b)² = a² + 2ab + b² (page 70). It can be used to square binomial expressions and to do numerical calculations (page 71), and to factorise expressions such as x² + 4x + 4 = (x + 2)² (page 72).
- (a − b)² = a² − 2ab + b², found by replacing b with −b; the book squares 29 as (30 − 1)² (page 73).
- a² − b² = (a + b)(a − b) (page 77).
- To factorise x² + px + q, write it as x² + (a + b)x + ab and look for a and b with a + b = p and ab = q (pages 80 and 81).
- (a + b)³ = a³ + 3a²b + 3ab² + b³ (page 82).
Quick numbers with identities
Question 1. Use (a + b)² = a² + 2ab + b² to find 61².
Answer: 3721. 61 = 60 + 1, so 61² = 60² + 2 × 60 × 1 + 1² = 3600 + 120 + 1 = 3721. (Using the identity for numerical calculations, page 71.)
Question 2. Use (a − b)² = a² − 2ab + b² to find 49².
Answer: 2401. 49 = 50 − 1, so 49² = 50² − 2 × 50 × 1 + 1² = 2500 − 100 + 1 = 2401. (The identity and the same method used for 29², page 73.)
Question 3. Use a² − b² = (a + b)(a − b) to find 96 × 104.
Answer: 9984. 96 = 100 − 4 and 104 = 100 + 4, so 96 × 104 = (100 − 4)(100 + 4) = 100² − 4² = 10000 − 16 = 9984. (Page 77.)
Expanding and factorising
Question 4. Expand (3x + 4y)².
Answer: 9x² + 24xy + 16y². Take a = 3x and b = 4y: (3x)² + 2(3x)(4y) + (4y)² = 9x² + 24xy + 16y². (Squaring a binomial expression, page 71.)
Question 5. Factorise x² + 10x + 25.
Answer: (x + 5)². x² + 10x + 25 = x² + 2 × x × 5 + 5², which is a² + 2ab + b² with a = x and b = 5. So it equals (x + 5)². (Factorisation using identities, page 72.)
Question 6. Factorise x² + 9x + 20.
Answer: (x + 4)(x + 5). Compare x² + 9x + 20 with x² + (a + b)x + ab: we need a + b = 9 and ab = 20. The pair 4 and 5 works, since 4 + 5 = 9 and 4 × 5 = 20. So x² + 9x + 20 = (x + 4)(x + 5). (Pages 80 and 81.)
Using an identity backwards, and a cube
Question 7. If x + y = 8 and xy = 15, find x² + y².
Answer: 34. From (x + y)² = x² + 2xy + y², we get x² + y² = (x + y)² − 2xy = 8² − 2 × 15 = 64 − 30 = 34. Check: x = 3 and y = 5 give 9 + 25 = 34. (The identity, pages 70 and 71.)
Question 8. Use (a + b)³ = a³ + 3a²b + 3ab² + b³ to find 11³.
Answer: 1331. 11 = 10 + 1, so 11³ = 10³ + 3 × 10² × 1 + 3 × 10 × 1² + 1³ = 1000 + 300 + 30 + 1 = 1331. (Finding new identities, page 82.)
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 9 Exploring Algebraic Identities questions, a separate short set on the same chapter.
- Printable worksheet with answer key, in English, Hindi and Marathi: Class 9 Exploring Algebraic Identities worksheet.
- The chapter before this one, in the same style: Class 9 The World of Numbers, 8 practice questions.
- Where factorising comes back in Class 10: Class 10 Polynomials and Class 10 Quadratic Equations.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 67.
- NCERT, Ganita Manjari: Textbook of Mathematics for Grade 9, Part I (First Edition, April 2026), Chapter 4 "Exploring Algebraic Identities", printed pages 68-91 (what an identity is and (a + b)², page 70; squaring binomials and numbers, page 71; factorisation using identities, page 72; (a − b)² and 29², page 73; a² − b² = (a + b)(a − b), page 77; factorising x² + (a + b)x + ab, pages 80-81; (a + b)³, page 82): ncert.nic.in/textbook/pdf/iemh104.pdf
- NCERT, Ganita Manjari: Textbook of Mathematics for Grade 9, Part I, front matter and contents (chapter titles and starting pages): ncert.nic.in/textbook/pdf/iemh1ps.pdf
The identities and methods are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.