Basic Math Class (Number Part-III)
Numbers-III VI. MULTIPLICATION BY SHORT CUT METHODS 1. Multiplication By Distributive Law : (i) a x (b + c) = a x b + a x c (ii) a x (b-c) = a x b-a x c. Ex. (i) 567958 x 99999 = 567958 x (100000 - 1) = 567958 x 100000 - 567958 x 1 = (56795800000 - 567958) = 56795232042. (ii) 978 x 184 + 978 x 816 = 978 x (184 + 816) = 978 x 1000 = 978000. 2. Multiplication of a Number By 5 n : Put n zeros to the right of the multiplicand and divide the number so formed by 2 n Ex. 975436 x 625 = 975436 x 5 4 = 9754360000 = 609647600 VII. BASIC FORMULAE 1. (a + b) 2 = a 2 + b 2 + 2ab 2. (a - b) 2 = a 2 + b 2 - 2ab 3. (a + b) 2 - (a - b) 2 = 4ab 4. (a + b) 2 + (a - b) 2 = 2 (a 2 + b 2