Suppose: m * n = a 2-b 2 According to this law, that is:
a-b=m a+b=n
Simultaneous solution: a=(m+n)/2 b=(n-m)/2
So:
m*n=[(m+n)/2]^2 - [(n-m)/2]^2
This is the general formula.
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Proof: Right = (m 2+2mn+n 2)/4-(m 2-2mn+n 2)/4
=mn
= left
So it is established.