Wednesday, January 9, 2008

A Visualization for Factoring the Difference of Two Squares

M2 - N2 = (M+N)(M-N)

Given that my difference of squares problem from yesterday may have been overly ambitious for middle schoolers (and I will have more to say about that in the comments section from that post), I thought it was worth reviewing a diagram that many of you have probably seen before. There are many similar geometric representations of standard factoring and distributive formulas in algebra, but this one has always been one of my favorites. It would be more effective if I had been able to shade rectangles R and S using different colors, but I did the best I could on short notice.
It's often a good exercise for algebra students to invent similar diagrams for other formulas, although the use of manipulatives such as algebra tiles can be even more effective.


Anonymous said...


Dave Marain said...

I'm not sure everyone would appreciate this! For students, the diagram might be helpful, although I think colored 'algebra bars' would be even more instructive. Kinda' like a puzzle for students to take apart and rearrange. They can label the sides of each square or rectangle and make the formula prove itself! Are you in the classroom to try this out with students? If so, let me know how it goes.