Cool math shortcuts

[Morgan O'Mally]

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While teaching some boring Algebra stuff today (FOIL and factoring) I came up with a math shortcut that I thought was kind of cool. Anyway, one problem was to expand (x-2)(x+2) (it is x^2 - 2x + 2x - 4, or x^2 - 4). My brain started to wander and I was thinking that means x^2 = (x-2)(x+2) + 4. So, if you wanted to square a number like 98, you could do 100*96, then add 4 to get 9604. In fact, you could generalize the formula:

x^2 = (x-a)(x+a) + a^2

So, if you wanted to square 94, you could make a = 6 and do 100*88 + 36 = 8836.

Anyway, does anyone know of any other shortcuts like this or of a book I could get to learn how to solve problems more quicky in my head. It doesn't really serve any purpose other than to entertain myself, but I'm curious if there is something like this out there.

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square 37 for me using your shortcut

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Was waiting for this.

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It still works and serves its purpose of making it such easier to do in your head. Normally if I had to do this in my head I'd do 900 + 210 + 259, but Homer's way is much faster and simpler.

GoT

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My boy is Wicked Smart!