When multiplying binomials and working with polynomials, sometimes we come up with polynomial special products. Examples of a special polynomial products include perfect square trinomials (a^2 + 2ab + b^2) and polynomials where the inner and outer terms are additive inverses and cancel each other out (a^2 - b^2). Knowing these types of special product patterns help us easily solve polynomial problems.
When you're multiplying binomials, there's a couple things that we call special cases.
One special case is when you get a perfect square trinomial. A perfect square trinomial is the result of squaring a binomial, ulet me show you what that looks like. If I have a binomial like a+b and I square it, which means multiplying it by itself, so you could write it like this also, my answer always looks like a squared plus 2ab plus b squared always always always when I take a binomial and I square it my answer looks like this we call this a perfect square trinomial because took binomial and squared it. That's one special products that you're going to see.
Another one you're going to see that's one of my personal favorites is if I do a product like a+b multiplied by a-b. If I would FOIL or do a rectangle my inner and outer terms would be eliminated they'll be added as inverses. Here's what I'm talking about, b times a my inners, and negative b times a my outers are additive inverses they cancel each other out my final answer for this kind of product always looks like a squared take away b squared. That's another one of my personal favorites.
These are called special cases and you're going to see a lot of problems that have this type of answer only not going to always use the letters a and b. It might be like x and y or 2x and y or 2x and 4 something like that, but when you have these kinds of patterns in your original problem like a squared binomial or a plus and a minus where the terms are the same otherwise you're going to get these special results, so keep that in minds when you're working through your homework when you're multiplying binomials and trinomials.