IM Alg2.2.23 Lesson: Polynomial Identities (Part 1)
Calculate the following differences:
What do you notice about these calculations?
Clare thinks the difference between the squares of two consecutive integers will always be the sum of the two integers. Is she right? Explain or show your reasoning. Pause here for a class discussion.
Andre thinks the difference between the squares of two consecutive even integers will always be 4 times the sum of the two integers. Is he right? Explain or show your reasoning.
Noah says that the difference of two cubes is always divisible by the difference of the two numbers. Do you agree with Noah?
Apply the distributive property to rewrite the following expressions without parentheses, combining like terms where possible.
What do you notice?