Class 9 CBSE Mathematics — Chapter 4: Exploring Algebraic Identities MCQs with Answers
90 practice questions · 30 Easy · 30 Medium · 30 Hard
Practise the most important Class 9 CBSE Mathematics questions from Chapter 4, "Exploring Algebraic Identities" — 9 separately timed quizzes built from 90 NCERT-aligned multiple-choice questions, with answers and explanations. The set is split into 30 Easy, 30 Medium and 30 Hard, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"Exploring Algebraic Identities" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+4 correct, −1 wrong, 0 skipped), training the accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Exploring Algebraic Identities, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below — answer and worked explanation — and signing in free opens all 90.
Key concepts: Exploring Algebraic Identities (Class 9 Mathematics)
An identity is an equation true for every value of the variable, so it can be used as a shortcut in both directions — to expand a product quickly, or to factorise an expression back into brackets. This chapter builds the square and cube identities, sees them as areas and volumes, and applies them to factorisation.
- Algebraic identity
- An equality that holds for every value of the variables, unlike an equation which holds only for particular values. This is why an identity can be applied to any numbers at all.
- Square of a sum
- (a + b)² expands to a² + 2ab + b². The middle term 2ab is the one most often dropped — squaring does not distribute across addition.
- Square of a difference
- (a − b)² expands to a² − 2ab + b². Only the middle term changes sign, because (−b)² is positive.
- Difference of squares
- a² − b² factorises as (a + b)(a − b). It turns awkward products such as 98 × 102 into 100² − 2² instantly.
Class 9 Mathematics Exploring Algebraic Identities MCQs with answers
14 solved questions across the difficulty levels this chapter is graded on — answer and explanation shown for each. The remaining 76 are timed and scored when you sign in.
- Q1Easy
Expand (x + 3)².
A.x² + 3x + 9B.x² + 9C.x² + 6x + 9✓ CorrectD.x² + 6x + 6Answer: C. x² + 6x + 9
Explanation: Use (a+b)² = a²+2ab+b² with a=x, b=3: x²+2(x)(3)+3² = x²+6x+9. A common slip is forgetting the middle term and writing x²+9, treating it like a²+b².
- Q2Easy
Expand (x − 5)².
A.x² − 10x + 25✓ CorrectB.x² − 25C.x² − 5x + 25D.x² + 10x + 25Answer: A. x² − 10x + 25
Explanation: Use (a−b)² = a²−2ab+b² with a=x, b=5: x²−2(x)(5)+25 = x²−10x+25. Dropping the middle term gives the tempting but wrong x²−25.
- Q3Easy
Expand (x + 4)(x − 4).
A.x² + 16B.x² − 16✓ CorrectC.x² + 8x − 16D.x² − 8x + 16Answer: B. x² − 16
Explanation: This fits the difference-of-squares pattern (a+b)(a−b) = a²−b²: x²−4² = x²−16. There is no middle term here, unlike the wrong x²+8x−16.
- Q4Easy
Which identity gives a² − b²?
A.(a + b)²B.(a − b)²C.(a + b)(a + b)D.(a + b)(a − b)✓ CorrectAnswer: D. (a + b)(a − b)
Explanation: a²−b² is the difference of squares, which factorises as (a+b)(a−b) — the cross terms +ab and −ab cancel. Squaring (a+b)² or (a−b)² instead leaves a middle 2ab term, so those aren't a pure difference.
- Q5Easy
(a + b)² is equal to:
A.a² + 2ab + b²✓ CorrectB.a² + b²C.a² − 2ab + b²D.2a + 2bAnswer: A. a² + 2ab + b²
Explanation: Squaring a sum gives (a+b)² = a²+2ab+b², with the middle term 2ab coming from the two cross products. Dropping it gives the common wrong shortcut a²+b².
- Q6Easy
Factorise x² − 9.
A.(x − 3)(x − 3)B.(x + 9)(x − 1)C.(x − 3)(x + 3)✓ CorrectD.(x + 3)(x + 3)Answer: C. (x − 3)(x + 3)
Explanation: x²−9 = x²−3² is a difference of squares, factorising as (x−3)(x+3). Writing (x−3)(x−3) instead would expand back to x²−6x+9, not x²−9.
- Q7Medium
Use an identity to evaluate 102².
A.10440B.10404✓ CorrectC.10204D.10004Answer: B. 10404
Explanation: Write 102 = 100+2 and apply (a+b)² = a²+2ab+b²: 100²+2(100)(2)+2² = 10000+400+4 = 10404. Skipping the doubled cross term 2(100)(2)=400 gives the wrong 10004.
- Q8Medium
Use an identity to evaluate 98².
A.9504B.9404C.9604✓ CorrectD.9904Answer: C. 9604
Explanation: Write 98 = 100−2 and apply (a−b)² = a²−2ab+b²: 100²−2(100)(2)+2² = 10000−400+4 = 9604. Mishandling the sign on the middle term is the usual source of error here.
- Q9Medium
Use an identity to evaluate 53 × 47.
A.2491✓ CorrectB.2501C.2391D.2481Answer: A. 2491
Explanation: Write 53×47 as (50+3)(50−3) = 50²−3² = 2500−9 = 2491, using the difference-of-squares pattern. Adding the squares instead of subtracting is the usual source of error here.
- Q10Medium
If a + b = 7 and ab = 12, what is a² + b²?
A.37B.49C.25✓ CorrectD.13Answer: C. 25
Explanation: Use a²+b² = (a+b)²−2ab: 7²−2(12) = 49−24 = 25. Forgetting to subtract 2ab and stopping at (a+b)² alone gives the wrong 49.
- Q11Medium
Factorise x² + 7x + 12.
A.(x + 2)(x + 6)B.(x + 3)(x + 4)✓ CorrectC.(x + 1)(x + 12)D.(x − 3)(x − 4)Answer: B. (x + 3)(x + 4)
Explanation: Look for two numbers that add to 7 and multiply to 12: 3 and 4 work, so x²+7x+12 = (x+3)(x+4). Picking 2 and 6 instead (product 12 but sum 8) gives the wrong (x+2)(x+6).
- Q12Hard
Expand (x + 2)³.
A.x³ + 6x² + 12x + 8✓ CorrectB.x³ + 8C.x³ + 2x² + 4x + 8D.x³ + 6x² + 8x + 8Answer: A. x³ + 6x² + 12x + 8
Explanation: Use (a+b)³ = a³+3a²b+3ab²+b³ with a=x, b=2: x³+3x²(2)+3x(4)+8 = x³+6x²+12x+8. Using single instead of tripled coefficients on the middle terms gives the wrong x³+2x²+4x+8.
- Q13Hard
Expand (x − 3)³.
A.x³ − 27B.x³ − 9x² + 27x − 27✓ CorrectC.x³ − 3x² + 9x − 27D.x³ − 9x² − 27x − 27Answer: B. x³ − 9x² + 27x − 27
Explanation: Use (a−b)³ = a³−3a²b+3ab²−b³ with a=x, b=3: x³−3x²(3)+3x(9)−27 = x³−9x²+27x−27. Using single instead of tripled coefficients gives the wrong x³−3x²+9x−27.
- Q14Hard
Factorise x³ + 8.
A.(x + 2)³B.(x + 2)(x² + 2x + 4)C.(x + 2)(x² − 4)D.(x + 2)(x² − 2x + 4)✓ CorrectAnswer: D. (x + 2)(x² − 2x + 4)
Explanation: x³+8 = x³+2³ fits the sum-of-cubes pattern a³+b³ = (a+b)(a²−ab+b²): (x+2)(x²−2x+4). Using a difference-of-squares shortcut instead gives the wrong (x+2)(x²−4).
Unlock the full chapter — free
You have 14 solved above — practise all 90 questions (30 Easy · 30 Medium · 30 Hard) with timed scoring and instant feedback, plus the complete key-concept notes, formulas & exam tips. Sign in with Google — no card needed.
Start this chapter free →Exploring Algebraic Identities — FAQs
What are the key concepts in Class 9 Mathematics Exploring Algebraic Identities?+
An identity is an equation true for every value of the variable, so it can be used as a shortcut in both directions — to expand a product quickly, or to factorise an expression back into brackets. This chapter builds the square and cube identities, sees them as areas and volumes, and applies them to factorisation. Key ideas include Algebraic identity, Square of a sum, Square of a difference, Difference of squares.
What does Class 9 Mathematics Chapter 4 (Exploring Algebraic Identities) cover on XamBaaz?+
It covers 90 NCERT-aligned MCQs on "Exploring Algebraic Identities" — 30 Easy, 30 Medium and 30 Hard — making 9 separately timed quizzes you can sit without ever repeating the same set, each with an instant explanation, suitable for CBSE Board exams and the JEE & NEET foundation years.
Are these "Exploring Algebraic Identities" questions free to practise?+
Yes — sign in with Google to practise "Exploring Algebraic Identities" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Exploring Algebraic Identities" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. There are 9 separately timed quizzes on this chapter, so you can come back and get a fresh set rather than re-sitting one you have seen. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Are these "Exploring Algebraic Identities" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to practise all 90 questions with instant scoring.
Is there negative marking in the "Exploring Algebraic Identities" quizzes?+
Yes — the timed quizzes use exam-grade marking: +4 for a correct answer, −1 for a wrong one and 0 for a skipped question. Note that MHT-CET and the CBSE board papers themselves carry no negative marking — our mocks for those are scored their way, not this way.
Are these important questions for Exploring Algebraic Identities?+
The set is curated to the NCERT syllabus and weighted toward the question patterns that actually appear in CBSE Board exams and the JEE & NEET foundation years, across Easy, Medium and Hard — so it doubles as an "important questions" revision list for "Exploring Algebraic Identities".