Factoring a Sum of Cubes

 A correspondent who teaches math to 9th graders writes:

I was looking at factoring the sum and difference of two cubes and was wondering if you have any input as to how to teach it for true understanding.

I have not taught this topic much, if at all, in Algebra 1, as it strikes me as rather technical, and better suited to older students.

My hunch is that one way to make this interesting is to present it as a puzzle to students who are familiar with “the box”, aka the generic rectangle, aka the multiplication table format. So here’s an off-the-cuff worksheet:

I’m guessing this could generate some good conversations. If you use it, or some version of it, I’d love to hear how it goes! If a student is frustrated, you might suggest doing the third one first.

–Henri

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