NCERT Solutions for Ganita Prakash (Part 1) Chapter 6 We Distribute, Yet Things Multiply

About this chapter

Distributivity, a (b + c) = ab + ac , is the one rule the whole chapter rests on. Read as an area picture, an a × ( b + c ) array splits into an a × b array and an a × c array. Applying it twice gives Identity 1: (a + m)(b + n) = ab + mb + an + mn — every term of the first bracket times every term of the second. Because the rules of integer multiplication handle the signs, the same identity also covers decreases: just take m or n negative. Three special cases are named in the chapter — 1A: (a + b)² = a² + 2ab + b², 1B: (a – b)² = a² + b² – 2ab, 1C: (a + b)(a – b) = a² – b². Each is proved twice: by expanding, and by cutting up a square. The same identities give fast mental arithmetic: 65² from 60² and 5², 397 × 403 from 400² – 3², and Sridharacharya's trick a² = (a + b)(a – b) + b². Sectio

• .1 Some Properties of Multiplication
• Fast Multiplications Using the Distributive Property
• .2 Special Cases of the Distributive Property
• Investigating Patterns
• .3 Mind the Mistake, Mend the Mistake
• .4 This Way or That Way, All Ways Lead to the Bay
• Coin Conjoin