Hello, this is Isaac Letz and this is my teaching demo video. So I will be doing my teaching demo video over a multiplying polynomials problem and it is one that I have commonly worked with algebra students in the past as a tutor on solving. Um, so here goes my demo. When I'm working with the student, I would typically have them, um, kind of work along the problem as much as they can showing me what they have learned in the class before I would jump into um, doing my own problem, but in the necessary case I would do so and then give them other example problems with different numbers, having me show, having them show me that they, um, have understood it. So when we look at multiplying polynomial at first, it can be a bit scary seeing the different XS and the different numbers, but what we have to remember when viewing a problem like this is that it's really just a simple multiplication problem.
So the way that we perform this multiplication problem actually is an acronym referred to as foil. And this is going to give us the order in which we do the multiplication problem. The F and FOIL stands for first, the O outside, the I inside and the L last. These are pretty easy to identify in the problem. This is our first one of this polynomial and this is our first one of this poral. So these will be multiplied and that will be one of my products, right? So at the end of the problem we are going to add the four products and combine the like terms. So my first product will be from multiplying the first terms. My second will be from the outside. So this is on the outside and this is on the outside. So I multiply my X square plus times my two.
Then comes my inside, I'll multiply my inside here, and this is my other inside. So these will be my third product. And then finally my last product is going to be the last times the last. So my three times my two. And during this multiplication we will start with the first x square times X. When we do this, which show this multiplication and give an individual three options for me. I would say, is it this, is it this, or is this the answer? And have them show me that they understand that multiplication of a variable with an exponent will be adding the exponents together. So if this doesn't have an exponent, that's kind of an unsaid one and that would show X three as the common answer as the correct answer. If they were having a bit of trouble understanding this, I would use it In terms of actual numbers showing this problem as a similar one, five squared times five.
If I had five cubed, this would be 1 25. If I had two five squared, this would be two times 25 would be 50. And I've had just X square, I would have five squared. This equal to 25. When I perform this problem, I get five squared. It's 25 times another five. This gives me 1 25. So from this we can see that x cube mics up, that correct answer and how that would be. So now we have our first product being xq. Then to find our second product, of course we're going to go multiply the outside. So I have my X squared and my two. That's going to give me two x squared. Then I would, then we have our insides. So we have three times X and I get three x. And then finally I have my last, which I have three times two. And this is going to gimme six to find my final answer, I will add all of these products combining like terms, separating those that are not. So I look, do I have any other X cubes? No, I don't. So that will be alone. Do I have any other X squareds? No, I do not. Speed by itself, do I have any three x, any single variables X to the first power? No, I do not. And then I have only one numerical value, and this would be my final answer for the problem.
