XamBaaz
Try for Free

Exploring Algebraic Identities — Class 9 MCQs with Answers

Class 9 CBSE Mathematics · Chapter 4

90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated

Practise the most important Class 9 CBSE Mathematics questions from Chapter 4, "Exploring Algebraic Identities". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.

To score well in "Exploring Algebraic Identities", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.

Use this chapter for focused revision. Start with the Easy set to check your basics on Exploring Algebraic Identities, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.

Exploring Algebraic Identities — important questions & MCQs with answers (Class 9 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

  1. Q1Easy

    Expand (x + 3)².

    Show answer

    Answer: 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.

  2. Q2Easy

    Factorise x² − 9.

    Show answer

    Answer: (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.

  3. Q3Medium

    Simplify (x² − 4)/(x + 2), where x ≠ −2.

    Show answer

    Answer: x − 2

    Explanation: Factor the numerator: x²−4 = (x−2)(x+2), so dividing by (x+2) cancels that factor and leaves x−2. Cancelling terms without factoring first leads to the wrong x−4.

  4. Q4Medium

    Use an identity to evaluate 102².

    Show answer

    Answer: 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.

  5. Q5Hard

    Simplify (x² − 9)/(x + 3), where x ≠ −3.

    Show answer

    Answer: x − 3

    Explanation: Factor the numerator: x²−9 = (x−3)(x+3), so dividing by (x+3) cancels that factor and leaves x−3. Cancelling terms without factoring first leads to the wrong x−9.

  6. Q6Hard

    Simplify (x + y)³ − (x − y)³.

    Show answer

    Answer: 6x²y + 2y³

    Explanation: Expand both cubes: (x³+3x²y+3xy²+y³)−(x³−3x²y+3xy²−y³) = 6x²y+2y³, since the x³ and 3xy² terms cancel while the x²y and y³ terms double. Assuming the x²y term also cancels gives the wrong 2y³ alone.

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.
Two pictures, one above the other. Top: a square of side a with a small square of side b removed from its top-right corner (shown dashed), leaving an L-shape of area a² − b², made of a rectangle a by (a − b) and a rectangle (a − b) by b. An arrow points down to the second picture: the same two pieces placed side by side form one rectangle of length a + b and width a − b, of area (a + b)(a − b).
Area model (visualisation)
Drawing a square of side (a + b) and splitting it into an a² square, a b² square and two ab rectangles shows geometrically why (a + b)² = a² + 2ab + b².
A big square whose side is split into a part a and a part b along the bottom and the left side; the whole top side is marked a + b. It is cut into four pieces: a square marked a² (bottom left), two rectangles each marked ab, and a small square marked b² (top right). Adding the pieces gives (a + b)² = a² + 2ab + b².
Square of a trinomial
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca — each term squared, plus twice every pair product.
A big square whose side is split into parts a, b and c, marked along the bottom and the left side. Lines through the split points cut it into nine pieces: three squares a², b² and c² on the diagonal, and two rectangles each of ab, bc and ca. So (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
Cube of a sum
(a + b)³ = a³ + b³ + 3ab(a + b), a compact form that is usually faster than multiplying the bracket out three times.
Cube of a difference
(a − b)³ = a³ − b³ − 3ab(a − b), the same structure with alternating signs.
Sum and difference of cubes
a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²). Note the middle sign of the quadratic factor is the opposite of the bracket's.
Factorisation
Rewriting an expression as a product. Always take out the highest common factor first, then look for a recognisable identity in what remains.
Factorising a quadratic by splitting
For x² + px + q, find two numbers that multiply to q and add to p, split the middle term with them, then group in pairs.
Factorisation by grouping
When four terms share no single common factor, group them in pairs, factor each pair, and extract the bracket that both pairs now share.
Simplifying rational expressions
Factorise numerator and denominator, then cancel the common factors. Only whole factors cancel, never individual terms of a sum.
7 formulas and exam tips — free with sign-in.

Start this chapter free

You have 6 to try above. Sign in with Google (no card needed). You get 1 Easy + 1 Medium quiz on every chapter, free for good — plus a free Hard quiz when you score 70%+ on a Medium quiz (1 per subject), and the formulas & exam tips.

This chapter has 90 questions (30 Easy · 30 Medium · 30 Hard), with timed scoring and instant feedback. The rest unlock with the ₹999/year plan.

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, Area model (visualisation), Square of a trinomial.

What does Class 9 Mathematics Chapter 4 (Exploring Algebraic Identities) cover on XamBaaz?+

It has 90 NCERT-based MCQs on "Exploring Algebraic Identities": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare 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. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.

How should I revise "Exploring Algebraic Identities" for the exam?+

Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.

Are these "Exploring Algebraic Identities" MCQs available with answers?+

Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.

Is there negative marking in the "Exploring Algebraic Identities" quizzes?+

Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.

What are the important questions from Exploring Algebraic Identities (Class 9 Mathematics)?+

The questions that matter most test Algebraic identity, Square of a sum, Square of a difference, Difference of squares, Area model (visualisation), Square of a trinomial. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.

Is there an online quiz for Exploring Algebraic Identities?+

Yes — Class 9 Mathematics Exploring Algebraic Identities has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.

More Class 9 Mathematics chapters

Class 9 — other subjects

← All Class 9 Mathematics chapters
🦅 One new exam question every day on Instagram — Follow @xambaaz