Today we're going to look at some special things when we're given polynomials in certain forms. For the first half of the lesson, we'll look at special products.
There are three types of special products, and I use F and L in the formulas because F stands for first and L stands for last. You might see these formulas elsewhere with x and y or a and b, but I think they make more sense using F and L:
Sum and Difference of Terms: (F + L)(F – L) = F^2 – L^2
Square of a Binomial (Sum): (F + L)^2 or (F + L)(F + L) = F^2 + 2FL + L^2
Square of a Binomial (Difference): (F – L)^2 or (F – L)(F – L) = F^2 – 2FL + L^2
We call these special products because we have special shortcuts to multiply them, and we do not have to rely on FOILing them. We want to have a good understanding of these because they'll become important in factoring, as well as other scenarios.
Take a look at some of the example problems in the following link:
Once you feel comfortable with these special products, you can watch the following videos to see how these relationships give us new ways of factoring polynomials:
Videos: Factoring Special Forms
I will be honest with you. Right now, the most important part of this lesson is understanding how to factor a difference of two squares. However, the other two special forms become important later when we're completing the square and when we look at equations that give us graphs of circles. So you still want to be familiar with them to be better prepared for future lessons.
Finally, remember to complete the homework assignment titled "Special Products and Special Forms" which is available on WebAssign.