Math visualization: Multiplying Two Binomials

In my earlier post Math visualization: (x + 1)², I showed how to draw a picture that proved the equality

(x + 1)² = x² + 2x + 1

An alert reader commented that (x + 1)² is a specific instance of the binomial squared

(x + a)² = x² + 2ax + a²

Here's a visualization of that equality:



It turns out that the illustration can be generalized a little bit further to cover multiplying two binomials that form a rectangle (not just a perfect square).

(x + a)(x + b) = x² + ax + bx + ab

If you want to see how this idea can be extended into the third dimension, check out Montessori World's page on the Binomial Cube.