On: A visual proof that a^2 – b^2 = (a + b)(a – b)

[chisquared]

> 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).