Polynomial Identities and Proofs

Question

lukecrayonz · Answer

"You are going to design an advertisement for a new polynomial identity that you are going to invent. Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof in an engaging way! Make it so the whole world wants to purchase your polynomial identity and can't imagine living without it!"

lukecrayonz · Answer

attachment

lukecrayonz · Answer

So I can't use..
Pythagorean triplets, sum of cubes, diff of squares, square of a binomial, and diff of cubes

directrix · Answer

Check out the "Secret Lives of Polynomial Identities." I can't say that it will help but you never know. http://www.math.uiuc.edu/~reznick/63011.pdf

directrix · Answer

If you prefer video, http://www.youtube.com/watch?v=4g36wgmCtLM

lukecrayonz · Answer

This literally makes no sense haha

lukecrayonz · Answer

@Directrix I'll skip it for now, help with a different one :O
Where do they make errors?

directrix · Answer

I don't follow how Theo went from the second to the third step. Do you see an error?

lukecrayonz · Answer

Hmm and what did Paula do wrong?

lukecrayonz · Answer

Factored incorrectly in step 5

directrix · Answer

Check Paula's multiplication in blue and her factoring in green.