CBSE Class 9 Maths Chapter 4: Exploring Algebraic Identities — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 4: Exploring Algebraic Identities from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): An algebraic identity is an equation true for every permissible value of its variables.
Reason (R): Unlike an equation satisfied only by particular values, an identity remains valid throughout its domain.
Reason (R): Unlike an equation satisfied only by particular values, an identity remains valid throughout its domain.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Universal validity is the defining feature of an identity.
2
Assertion (A): Algebra tiles can be used to visualise and factor certain identities.
Reason (R): Identities can also simplify numerical products and powers.
Reason (R): Identities can also simplify numerical products and powers.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true uses of identities, but numerical simplification does not explain the algebra-tile model.
3
Assertion (A): The identity (x - y)^2 = x^2 - 2xy + y^2 is valid for all real x and y.
Reason (R): The middle term in this expansion is +2xy.
Reason (R): The middle term in this expansion is +2xy.
Answer: (c)
A is true, but R is false. Subtracting y produces the negative middle term -2xy.
4
Assertion (A): The identity (x + y)^2 = x^2 + y^2 is valid for all x and y.
Reason (R): The correct expansion includes the additional middle term 2xy.
Reason (R): The correct expansion includes the additional middle term 2xy.
Answer: (d)
A is false, but R is true. Squaring a sum creates two cross-products xy.
5
Assertion (A): The expression x^2 - y^2 factors as (x + y)(x - y).
Reason (R): Multiplying the conjugate binomials cancels the opposite xy terms.
Reason (R): Multiplying the conjugate binomials cancels the opposite xy terms.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The remaining terms are x^2 and -y^2.
6
Assertion (A): The expansion of (x + y + z)^2 includes x^2 + y^2 + z^2 and twice each pairwise product.
Reason (R): The identity (x + y)(x - y) = x^2 - y^2 is also valid.
Reason (R): The identity (x + y)(x - y) = x^2 - y^2 is also valid.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both identities are correct, but the difference-of-squares identity does not explain the trinomial-square expansion.
7
Assertion (A): The product (x + a)(x + b) equals x^2 + (a + b)x + ab.
Reason (R): Its constant term is a + b.
Reason (R): Its constant term is a + b.
Answer: (c)
A is true, but R is false. The constant term is ab; a + b is the coefficient of x.
8
Assertion (A): In (ax + b)(cx + d), the coefficient of x is ac + bd.
Reason (R): The correct middle coefficient is ad + bc.
Reason (R): The correct middle coefficient is ad + bc.
Answer: (d)
A is false, but R is true. The products ac and bd contribute to x^2 and the constant term, respectively.
9
Assertion (A): The difference of cubes factors as x^3 - y^3 = (x - y)(x^2 + xy + y^2).
Reason (R): Expanding the factors cancels the mixed terms and leaves x^3 - y^3.
Reason (R): Expanding the factors cancels the mixed terms and leaves x^3 - y^3.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Direct multiplication verifies the factorisation.
10
Assertion (A): The expansions of (x + y)^3 and (x - y)^3 contain binomial coefficients 1, 3, 3, 1.
Reason (R): The sum-of-cubes identity factors x^3 + y^3 using a linear factor x + y.
Reason (R): The sum-of-cubes identity factors x^3 + y^3 using a linear factor x + y.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the sum-of-cubes factorisation does not explain the binomial coefficients.
11
Assertion (A): The factorisation x^3 - y^3 = (x - y)(x^2 + xy + y^2) is correct.
Reason (R): The expression x^3 - y^3 has x + y as a factor for all x and y.
Reason (R): The expression x^3 - y^3 has x + y as a factor for all x and y.
Answer: (c)
A is true, but R is false. The general linear factor is x - y, not x + y.
12
Assertion (A): The sum of cubes factors as x^3 + y^3 = (x + y)(x^2 + xy + y^2).
Reason (R): The correct second factor is x^2 - xy + y^2.
Reason (R): The correct second factor is x^2 - xy + y^2.
Answer: (d)
A is false, but R is true. The negative middle term is necessary for the mixed terms to cancel.
13
Assertion (A): A rational algebraic expression may be simplified by cancelling a common non-zero factor from numerator and denominator.
Reason (R): Factorisation exposes common multiplicative factors that can be cancelled without changing the value on the permitted domain.
Reason (R): Factorisation exposes common multiplicative factors that can be cancelled without changing the value on the permitted domain.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The restriction keeps the cancelled factor and original denominator away from zero.
14
Assertion (A): A quadratic expression can be factorised algebraically by splitting its middle term when suitable numbers are found.
Reason (R): Algebra tiles can represent terms such as x^2, x, and constants geometrically.
Reason (R): Algebra tiles can represent terms such as x^2, x, and constants geometrically.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are valid factorisation approaches, but the tile representation does not explain the algebraic splitting method.
15
Assertion (A): A common factor may be cancelled from the numerator and denominator when it is non-zero.
Reason (R): The cancellation remains valid even at values where the cancelled factor equals zero.
Reason (R): The cancellation remains valid even at values where the cancelled factor equals zero.
Answer: (c)
A is true, but R is false. At such values the original expression is undefined, so they must remain excluded.
16
Assertion (A): Terms joined by addition may always be cancelled directly across a fraction bar.
Reason (R): Cancellation applies to common multiplicative factors after appropriate factorisation.
Reason (R): Cancellation applies to common multiplicative factors after appropriate factorisation.
Answer: (d)
A is false, but R is true. Additive terms cannot be removed unless the expressions are first rewritten as products with a common factor.
17
Assertion (A): Identities can simplify calculations such as 104 x 96 by rewriting the numbers around a convenient base.
Reason (R): The product can be treated as (100 + 4)(100 - 4) and evaluated using a difference of squares.
Reason (R): The product can be treated as (100 + 4)(100 - 4) and evaluated using a difference of squares.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The identity gives 100^2 - 4^2 without long multiplication.
18
Assertion (A): A valid algebraic identity remains true when variables are assigned negative values within its domain.
Reason (R): Factorisation can be regarded as reversing an expansion.
Reason (R): Factorisation can be regarded as reversing an expansion.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the reverse-expansion viewpoint does not explain why identities accept negative substitutions.
19
Assertion (A): The identity x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) holds for all x, y, and z.
Reason (R): It holds only when x + y + z = 0.
Reason (R): It holds only when x + y + z = 0.
Answer: (c)
A is true, but R is false. When the sum is zero the left side is zero, but the displayed equality is an identity valid generally.
20
Assertion (A): A rational algebraic expression is defined even when its denominator equals zero.
Reason (R): Values that make the denominator zero must be excluded from its domain.
Reason (R): Values that make the denominator zero must be excluded from its domain.
Answer: (d)
A is false, but R is true. Division by zero is undefined, regardless of any later algebraic simplification.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 4 Exploring Algebraic Identities?
This chapter covers all key topics from Exploring Algebraic Identities as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
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