Students will learn how to expand a product of two binomials, such as (2x + 4)(x + 5). They will learn how to do this in four different ways: by using algebra tiles, by using the box method, by crossing lines, by distributing, and by using FOIL. I'm not sure in what order these should be taught, but I'm confident that expanding by crossing lines should be taught last, as it's intriguing, but not very useful. Here's a video on using the box method. After that, show students how expanding a product of two binomials can be used to square large numbers. For example, \(103^2 = (100 + 3)^2.\) Finally, give your students this challenge, then this one. Finding the equation necessary to solve that last challenge is quite difficult. Your students may need some hints along the way.