Sunday, January 10, 2010

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.

1 comment:

stockwellapril said...

I love this technique. I think people are starting to use this over the FOIL method because it's such a great visualization of how to multiply binomials.

For a different perspective, I just blogged about the FOIL method: