(X)(Y) = (N-X)(N-Y) + N(X+Y-N)
This is representation of how we used to teach children multiplication on their ten fingers by overlapping two numbers from opposite sides and multiplying the resulting left with right, and adding that to the number in the middle (multiplied by ten).
My question, is there values where N does not apply?
http://lifehacker.com/5942037/quickly-multiply-single-digit-numbers-with-your-hands
Ian Kennedy
If you expand the right hand side of your equation, you get
n2 -nx -ny +xy +nx +ny -n2
Simplifying
= +xy
So the equation is true for all N. Some values N are just more convenient e.g. N=10.
If you are teaching children with no thumbs, they can use N= 8 to do octal multiplication.
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