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by chisquared 545 days ago
> Then you've just skipped the case when a^2 - b^2 is negative.

Not really. If b > a, then swap them to conclude that b^2 - a^2 = (b + a)(b - a), which is what the visual proof demonstrates.

Your conclusion is equivalent to saying that a^2 - b^2 = (a + b)(a - b).