CBSE Class 8 Maths Chapter 6: We Distribute, Yet Things Multiply — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 6: We Distribute, Yet Things Multiply from the NCERT Class 8 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): The distributive property states a(b + c) = ab + ac.
Reason (R): Multiplication by a applies to each term inside the sum.
Reason (R): Multiplication by a applies to each term inside the sum.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Distributing the factor gives the right-hand expression.
2
Assertion (A): The expression 7 x 98 can be evaluated as 7(100 - 2).
Reason (R): The square of 10 is 100.
Reason (R): The square of 10 is 100.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the square fact does not explain the chosen decomposition of 98.
3
Assertion (A): The expression a(b - c) equals ab - ac.
Reason (R): The factor a multiplies only b and not c.
Reason (R): The factor a multiplies only b and not c.
Answer: (c)
A is true, but R is false. Distributivity applies the factor to both terms.
4
Assertion (A): The expression (a + b)c equals ac + b.
Reason (R): Distributivity gives ac + bc.
Reason (R): Distributivity gives ac + bc.
Answer: (d)
A is false, but R is true. Both addends receive the factor c.
5
Assertion (A): If one factor in xy increases by 1, the product increases by the other factor.
Reason (R): (x + 1)y - xy simplifies to y.
Reason (R): (x + 1)y - xy simplifies to y.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The distributive property proves the increment.
6
Assertion (A): Increasing both x and y by 1 changes xy to xy + x + y + 1.
Reason (R): The expression a(b + c) equals ab + ac.
Reason (R): The expression a(b + c) equals ab + ac.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the general distributive statement does not by itself explain the complete two-binomial expansion.
7
Assertion (A): The identity (a + b) squared includes the middle term 2ab.
Reason (R): It equals only a squared + b squared.
Reason (R): It equals only a squared + b squared.
Answer: (c)
A is true, but R is false. Expansion gives a squared + 2ab + b squared.
8
Assertion (A): The identity (a - b) squared equals a squared - b squared.
Reason (R): Expansion gives a squared - 2ab + b squared.
Reason (R): Expansion gives a squared - 2ab + b squared.
Answer: (d)
A is false, but R is true. The assertion omits two terms.
9
Assertion (A): The product (a + b)(a - b) equals a squared - b squared.
Reason (R): The cross terms -ab and +ab cancel.
Reason (R): The cross terms -ab and +ab cancel.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Cancellation leaves the difference of squares.
10
Assertion (A): The expression 99 squared can be evaluated using (100 - 1) squared.
Reason (R): The value is 9801.
Reason (R): The value is 9801.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the result does not explain why the identity is valid.
11
Assertion (A): The product (x + 3)(x + 4) equals x squared + 7x + 12.
Reason (R): Its constant term is 7.
Reason (R): Its constant term is 7.
Answer: (c)
A is true, but R is false. The constant term is 3 x 4 = 12.
12
Assertion (A): The product (2x + 1)(x + 3) equals 2x squared + 4x + 3.
Reason (R): Each term of the first binomial must multiply each term of the second.
Reason (R): Each term of the first binomial must multiply each term of the second.
Answer: (d)
A is false, but R is true. The correct middle coefficient is 7: 2x squared + 7x + 3.
13
Assertion (A): Factoring reverses distributive expansion.
Reason (R): The expression ab + ac can be written a(b + c).
Reason (R): The expression ab + ac can be written a(b + c).
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The common factor a is extracted.
14
Assertion (A): The expression 6x + 9 has common factor 3.
Reason (R): The identity (a - b)(a + b) equals a squared - b squared.
Reason (R): The identity (a - b)(a + b) equals a squared - b squared.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the difference-of-squares identity does not explain this common factor.
15
Assertion (A): The difference x squared - 25 factors as (x - 5)(x + 5).
Reason (R): It factors as (x - 5) squared.
Reason (R): It factors as (x - 5) squared.
Answer: (c)
A is true, but R is false. The difference-of-squares factors have opposite signs.
16
Assertion (A): The expression x squared + 10x + 25 cannot be factored.
Reason (R): It is the perfect square (x + 5) squared.
Reason (R): It is the perfect square (x + 5) squared.
Answer: (d)
A is false, but R is true. The trinomial matches a squared + 2ab + b squared.
17
Assertion (A): Two algebraic methods giving different simplified results signal an error in at least one method.
Reason (R): Equivalent valid transformations must preserve the expression's value.
Reason (R): Equivalent valid transformations must preserve the expression's value.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Consistency is a useful check on symbolic work.
18
Assertion (A): Substitution can test whether two expressions may be unequal.
Reason (R): One input giving different values proves the expressions are not identical.
Reason (R): One input giving different values proves the expressions are not identical.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the second describes the counterexample principle rather than every substitution purpose.
19
Assertion (A): Checking one numerical value cannot prove two expressions are identical for all x.
Reason (R): Agreement at one input always proves an identity.
Reason (R): Agreement at one input always proves an identity.
Answer: (c)
A is true, but R is false. Different expressions may coincide at a particular input.
20
Assertion (A): Distributivity works only for positive integers.
Reason (R): The algebraic law holds for rational numbers and other ordinary number systems as well.
Reason (R): The algebraic law holds for rational numbers and other ordinary number systems as well.
Answer: (d)
A is false, but R is true. The property is not restricted by sign.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply?
This chapter covers all key topics from We Distribute, Yet Things Multiply as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 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 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
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