^{2}, I showed how to draw a picture that proved the equality

(x + 1)

^{2}= x^{2}+ 2x + 1An alert reader commented that (x + 1)

^{2}is a specific instance of the binomial squared

(x + a)

^{2}= x^{2}+ 2ax + a^{2}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) = x

^{2}+ ax + bx + abIf 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:

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:

http://blog.thinkwell.com/2010/07/prealgebra-multiplying-binomials.html

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