Visual proof ot the distributive property in $\mathbb{Z}$

Question

Is there a intuitive/visual (not formal) "proof" that the distributive property holds in $\mathbb{Z}$?

For the natural numbers $\mathbb{N}$ I know something like this:

There are two ways to get the total area $A$:

$a \cdot c + b \cdot c = A = (a + b) \cdot c$

Answer 1

I think that the same proof works fine for negative numbers -- just think of the plane as a large sheet of paper, and the rectangle you've drawn as a hole in it.

Finally, for $a⋅c - b⋅c = A = (a-b)⋅c$, assume that $b < a$, and draw two rectangles (where the $b⋅c$ rectangle is a 'hole' in the $a⋅c$ rectangle).