Extra Questions: Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply

Practice questions beyond the textbook exercises, testing deeper understanding of the distributive property and algebraic identities for Class 8 Maths Chapter 6: We Distribute, Yet Things Multiply. These Class 8 Mathematics Chapter 6 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Extra Questions: Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply

1. 1 (Assertion-Reason). Assertion: (x+7)² and (x−7)² differ by 28x. Reason: (a+b)²−(a−b)² = 4ab.
   Solution: Both true, and the reason correctly explains the assertion — (a+b)²−(a−b)²=4ab, so with a=x, b=7 the difference is 4×x×7=28x.
2. 2 (Numerical). Find the value of 998² using a suitable identity.
   Solution: 998² = (1000−2)² = 1000000−4000+4 = 996004.
3. 3 (Short Answer). Is (a+b)³ the same as a³+b³?
   Solution: No — (a+b)³ = a³+3a²b+3ab²+b³, which has two extra cross terms not present in a³+b³.
4. 4 (Applied). A square garden of side (x+5) m has a square flower bed of side x m cut from one corner. Find the remaining area.
   Solution: Remaining area = (x+5)²−x² = x²+10x+25−x² = (10x+25) m².
5. 5 (Assertion-Reason). Assertion: 205×195 can be found quickly using a difference-of-squares identity. Reason: 205×195 = (200+5)(200−5) = 200²−5².
   Solution: Both true, and the reason correctly explains the assertion — 200²−5² = 40000−25 = 39975.
6. 6 (Numerical). Two consecutive even numbers have squares differing by 84. Find the numbers.
   Solution: Let the numbers be 2n and 2n+2. (2n+2)²−(2n)² = 8n+4 = 84 ⇒ n=10. The numbers are 20 and 22 (22²−20²=484−400=84).
7. 7 (Synthesis). If a+b=10 and ab=21, find a²+b².
   Solution: a²+b² = (a+b)²−2ab = 100−42 = 58.
8. 8 (Applied). Simplify 104×96 using a suitable identity.
   Solution: 104×96 = (100+4)(100−4) = 10000−16 = 9984.
9. 9 (Short Answer). Why is (x−y)² always non-negative, even when x−y itself is negative?
   Solution: Squaring removes the sign of any number, so (x−y)² = (y−x)² ≥ 0 regardless of whether x−y is positive or negative.
10. 10 (Assertion-Reason). Assertion: For any integer n, (n+1)²−(n−1)² is always a multiple of 4. Reason: (n+1)²−(n−1)² = 4n.
    Solution: Both true, and the reason correctly explains the assertion — the expression simplifies exactly to 4n, which is always a multiple of 4.

Frequently Asked Questions

How does the distributive law simplify multiplying a number by a sum of two terms?
Instead of first adding the two terms and then multiplying, the distributive law allows multiplying the outer number by each term separately and then adding the two products, which can make mental calculation easier, especially with larger numbers.

Why is understanding the distributive law important before learning to multiply two algebraic expressions with multiple terms?
Multiplying expressions with multiple terms, such as two binomials, relies on applying the distributive law repeatedly so that every term in one expression is multiplied with every term in the other before combining like terms.

Written by Satish

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