We Distribute, Yet Things Multiply

About this chapter

We Distribute, Yet Things Multiply is the sixth chapter of Class 8 Ganita Prakash Part 1. It uses the distributive property a(b + c) = ab + ac as a single thread to unify algebraic expansion, fast mental arithmetic, and pattern recognition. The chapter opens by asking how the product 23 × 27 changes when one or both numbers are increased by 1 — and answers it geometrically through a rows-and-columns diagram. From there it builds Identity 1, (a + m)(b + n) = ab + mb + an + mn, derives the three special cases (a + b)^2 = a^2 + 2ab + b^2, (a − b)^2 = a^2 − 2ab + b^2 and (a + b)(a − b) = a^2 − b^2, and uses them to compute 65^2, 55^2, 98 × 102, and 397 × 403 in one step. A 'Pinch of History' panel credits Brahmagupta's Brāhmasphuṭasiddhānta (628 CE, verse 12.55) with the first explicit statement of the distributive property — khanda-gunanam — and Sridharacharya (750 CE) with the identity a^2 = (a + b)(a − b) + b^2 used as a fast-squaring trick called ishta-gunana. CTET Paper 2 Mathematics tests this chapter through expansion items, identity-application word problems, mental-math shortcuts (× 11, × 101, × 99), and pedagogy items on like terms and the area-model. The four tests — Practice 15, Quiz 15, Hard 15, Mastery 30 — cover all six ideas at CTET depth and difficulty.