(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.