Difference of Two Squares (Part 2)

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 b is cut from a corner of a square of side a. By cutting the remaining figure in two and rearranging the pieces, a rectangle with side lengths of a+b and a-b can be formed, thus proving that a^2 - b^2 = (a+b)(a-b).

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.

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