Revision Notes: Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply

Class 8 Maths Chapter 6: We Distribute, Yet Things Multiply — Quick Revision Notes

• Distributive property: a(b+c) = ab+ac — the basis for expanding any product of multi-term expressions, term by term (e.g. (a+b)(c+d) = ac+ad+bc+bd).
• Identity 1A: (a+b)² = a²+2ab+b².
• Identity 1B: (a−b)² = a²−2ab+b²; and (a−b)² = (b−a)² always, since squaring removes the sign of the difference.
• Identity 1C: (a+b)(a−b) = a²−b² — the fastest identity for mentally multiplying two numbers equidistant from a round number, e.g. 397×403 = 400²−3².
• General difference-of-powers pattern: (a−b)(aⁿ+aⁿ⁻¹b+…+bⁿ) = aⁿ⁺¹−bⁿ⁺¹.
• Sum-of-squares identity: 2(a²+b²) = (a+b)²+(a−b)².
• All identities hold universally — for counting numbers, negative integers, and fractions alike — because they follow from pure algebraic expansion, not from any assumption about sign or type.
• Verifying a pattern with a few numbers is not a proof: claims about “always true” require a general algebraic derivation; a single counterexample is enough to disprove a claim.
• Applications: quick mental squaring/multiplication of numbers near a round number, expressing areas of composite geometric figures, and proving number patterns (e.g. middle-square-minus-neighbour-product = 1 for any three consecutive numbers).

Frequently Asked Questions

What does the distributive law state in algebra?
The distributive law states that multiplying a number by a sum is the same as multiplying that number by each term in the sum separately and then adding the results, expressed as a into (b plus c) equals ab plus ac.

Last Updated: September 23, 2026

How is the distributive law used when multiplying two algebraic expressions?
Each term in the first expression is distributed to multiply with every term in the second expression, and the resulting products are then combined by adding like terms together.

Written by Satish

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