It is observed that the difference between the two squares on the right of the equal sign is exactly the first number on the left and the sum is exactly the second number on the left.

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.