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).

Written by Satish

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