Tuesday, February 23, 2010

MULTIPLY

You only need seconds if you use and automate the use of the binomic formulas:

(x-y)(x+y) = x2 – y2 and (x+y)2 = x2 + 2xy + y2

then, e.g. : 83 * 87 = (85-2)(85+2) = (80+5)2 – 22 = (6400+800+25) – 4 = 7221

automated: take the square of the tens, add 10 time the tens, add 25, subtract the square of difference to the number with the ending five (i.e. 85-83=2), voila.

  1. 83 * 87 = 6400 + 800 + 25 – 4 = 7221
  2. 24 * 26 = 400 + 200 + 25 – 1 = 624
  3. 72 * 78 = 4900 + 700 + 25 – 9 = 5616
  4. 99 * 91 = 8100 + 900 + 25 – 16 = 9009
  5. 65 * 65 = 3600 + 600 + 25 – 0 = 4225

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