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I read an article the other day from this guy who claimed that -1 x -1 = +1 is 'evil' math. I understand where he is coming from with that statement, but -1 x -1 = +1 is not an arbitrary convention adopted by mathematicians to make everything fit in nicely. Calling it a 'rule' is a bit misleading too. There is a lot of smart people on this forum who *understand* why -1 x -1 = +1, so, if you are among this group of people, you need to read no further. But if you are curious, highlight to read:
Observe the following:
-1 x 0 = 0
Now -1 + 1 = 0. Replace the 0 on the left side of the previous expression by -1 + 1:
-1 x (-1 + 1) = 0
Now expand that expression:
(-1 x -1 ) + (-1 x 1) = 0