This week I learned a couple tricks to find the product of polynomials: a pattern for the product of simple binomials and an area model.

Pattern for simple binomials:

I think that it really helps because when you come across simple binomials (no coefficients on x’s), you won’t have to spend too much time on it.

This is the pattern that I found to make multiplying simple binomials easier:

  1. For the fist term: multiply the x’s together (always make x^2 with simple binomials)
  2. Second term: add the constants together and add an x
  3. Third term: multiply the constants together

Example:

Area models:

An area model is a simple way to organize and find the product of polynomials. I think it is important to learn because it keeps your work organized, you won’t likely miss one of the terms and you can use it with any type of polynomial. The catch is that it only works when you multiply 2 polynomials together.

The way it works:

  1. Make a rectangle
  2. Divide it into how may terms in each polynomial on each side
  3. Multiply the terms, like in a multiplication table
  4. Simplify the answer

Pro tip:

If the question asks you to multiply more than 2 polynomials, either use FOIL to get it down to 2 or you can use the area model more than once.

Example: