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Is BGO an Elitist Society?

Posted By: Jason Lee
Date: Friday, 12 December 2008, at 2:19 a.m.

In Response To: Is BGO an Elitist Society? (Keene)

In his book, Art Benjamin describes what he calls the "close together method". It works for any two numbers, but the application of it is best for numbers that are close together.

The general formula you want to use is (x+a)(x+b) = x^2 + ax + bx + ab = x(x+a+b) + ab. So when multiplying (x+a)(x+b), choose x to be a nice number (a multiple of 10).

Let's say you want to multiply 14 * 17. Then x = 10, a = 4, and b = 7, so

14 * 17 = 10(10+4+7) + 4*7 = 10*21 + 28 = 210 + 28 = 238.

Another example: 38 * 43. Nothing stops you from choosing the variables to be negative, so I'll make x = 40, a = -2, and b = 3, so

38 * 43 = 40*(40-2+3) + (-2)(3) = 40*41 - 6 = 1640 - 6 = 1634.

JLee

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