Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials. Include common errors to watch out for when using each of these methods. Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.

As an added challenge, develop a model similar to algebra tiles that will allow you to show this multiplication. Describe an example of your model for the product (x + 1)(x2 + 2x + 2).
Imagine that you are teaching a new student how to multiply polynomials. Explain how multiplying polynomials is similar to multiplying integers. Then describe the key differences between the two.
If you multiply a binomial by a binomial, how many terms are in the product (before combining like terms)? What about multiplying a monomial by a trinomial? Two trinomials?

Write a statement about how many terms you will get when you multiply a polynomial with m terms by a polynomial with n terms. Give an explanation to support your statement.