In yesterday’s post, I discussed a numerical way for students in Algebra I to guess for themselves the formula for the difference of two squares.
There is a also well-known geometric way of deriving this formula (from http://proofsfromthebook.com/2013/03/20/representing-the-sum-and-difference-of-two-squares/)
The idea is that a square of side is cut from a corner of a square of side . By cutting the remaining figure in two and rearranging the pieces, a rectangle with side lengths of and can be formed, thus proving that .
Again, this is a simple construction that only requires paper, scissors, and a little guidance from the teacher so that students can discover this formula for themselves.