Students will start by using algebra tiles to factor quadratics which are a difference of squares. Two videos for factoring monic quadratics which are a difference of squares can be seen here and here. Students should start by factoring monic quadratics, the easiest of which is \(x^2 - 1.\) Once the method has been discovered, or if need be, taught, ask your students for a formula to factor \(x^2 - a^2.\) By factoring a couple quadratics, it's easy to infer that it's \((x + a)(x - a).\) Then ask your students to factor some non-monic quadratics, such as \(4x^2 - 9,\) and generalize their previous method and formula for \((bx)^2 - a^2.\) They should of course discover the answer is \((bx + a)(bx - a),\) which is again, easy to infer by factoring a couple non-monic quadratics.

Conclude by leading this investigation:

McGuire the Gathering (Multiplication, Patterns, Proof)

by MathPickle