If b is negative, define c = -b, and use the linked result to show that

a^2 - b^2 = a^2 - (-c)^2 = a^2 - c^2 = (a + c)(a - c) = (a + b)(a - b)

You can do this if you extend your concepts of length and area to signed quantities. You have to be clear to explain how the setup of the drawing works, but instead of cutting away a square of side b out of the corner of the square of side a, you might end up appending a negatively-signed square of side −b.