Write an algebraic proof showing that (a+b)(a-b)=a^2-b^2
for any a and b. (do not just plug in a bunch of numbers and call it good.)

for those of you who need a bit of a refresher about what a proof is, to do this, you will be showing every little algebra step needed to start with the expression (a+b)(a-b) and, by just changing one thing at a time using valid algebra steps in a well-organized way, end up with the expression a^2-b^2. you will need to give a reason why each step works. (reasons would be things like "distributive property of addition over multiplication","a x a =a^2 by the definition of an exponent". if you're not sure of the fancy math words why, try to give the best student-words reasons you can.) reasons should be centered around why you can do something rather than just using words to narrate your steps!
you can write a two-column proof, a paragraph proof, or a flowchart proof. if you're not sure what to, try to figure out the algebra steps first and then figure out why you're allowed to do those.
hint: the distributive property would be an excellent place to start!