Chapter 6 — We Distribute, Yet Things Multiply

Chapter 6 of the Class 8 Maths NCERT textbook (Ganita Prakash), "We Distribute, Yet Things Multiply", explores the distributive property of multiplication over addition and uses it to solve multiplication patterns, expand algebraic expressions, and develop fast multiplication techniques for special numbers.

• Distributive property as the engine — The chapter centres on distributing multiplication over addition to expand products of multi-term expressions and to predict how a product shifts when its factors are incremented or decremented.
• The three key identities — Students derive the square-of-a-sum, square-of-a-difference, and difference-of-squares identities as special cases of distribution, then verify them visually through rectangular area decomposition.
• Fast multiplication tricks — Distributivity is turned into mental-maths shortcuts for multiplying by 11, 101 and 1001, showing how one algebraic idea can describe the same pattern in several equivalent ways.

1. 01The distributive property: a(b + c) = ab + ac, and its extension (a + m)(b + n) = ab + mb + an + mn
2. 02When product ab is increased by 1 on one factor, the product increases by the other factor; when both increase by 1, the increase is a + b + 1
3. 03Square of sum identity: (a + b)² = a² + 2ab + b²
4. 04Square of difference identity: (a − b)² = a² − 2ab + b²
5. 05Difference of squares identity: (a + b)(a − b) = a² − b²
6. 06Fast multiplication rules using distributivity: multiply by 11 by adding adjacent digits; multiply by 101 by placing the number 100 places apart and adding the overlap
7. 07Algebraic identities can be verified and visualized geometrically using rectangular area decomposition