Anyway, area diagrams are pretty slick for teaching polynomial multiplication. Let's say you have (3x-2)(2x+4). Most of us probably learned FOIL, where you multiply the first, outside, inside and last. An area diagram for this would look like:
You then add up all your boxes, so you would have 6x2 + (-4x) + 12x + (-8), or 6x2+8x-8. The reason this is slick is that first off, it scales (FOIL only works for binomials). The other thing is that you can use it backwards when factoring. You can fill in the upper-left and lower-right hand corners, and then go through picking numbers that make the rest of the diagram work for your polynomial.