 This video is called Find the Area of the Shaded Region 1. When you look at this picture, you can see that we have a big rectangle and a smaller rectangle. To find the area of the shaded region, imagine that this big pink rectangle is one sheet of paper and we've cut out the smaller rectangle. So it's almost like you can see through the bigger rectangle in the small part, almost like an eye hole or something like that if this was a mask. So to find the area of the shaded region, it would make sense to find the area of the whole thing. So in this case, it would be the area of the big rectangle and then we're going to subtract out the area of the small, which in this case would be the white rectangle. So we will have two answers that we will then combine together using subtraction. So let's start by looking at the area of the big rectangle. We know a rectangle. To find the area, it's base times height. Well, I've got a base of 2x plus 5 and a height of 3x plus 1. So I have to foil first, outside, inside, last. 2x times 3x is 6x squared. 2x times 1 is a plus 2x. 5 times 3x is a plus 15x and 5 times 1 is plus 5. When I combine these like terms, I get 6x squared plus 17x plus 5. So that is the area of my big rectangle. So I could rewrite it up here if I wanted to. 6x squared plus 17x plus 5. Now let's go ahead and find the area of the small rectangle. Again, we'll have to foil. We will have x plus 2 times x. And actually, I won't have to foil this because it's a monomial times a binomial. So I'll just have to distribute x times x is x squared. x times 2 is a plus 2x. So my small rectangle is x squared plus 2x. I'm going to put that in parentheses simply to remind myself that when I'm subtracting the two polynomials, I have to remember that this negative applies to everything in my second polynomial. So I'm going to have to do a distributive property where this is really a negative 1. So I'm going to rewrite my first polynomial exactly as it is. 16x squared plus 17x plus 5. And then I distribute, I'm going to say minus x squared minus 2x. And now to finish, I'll combine like terms. I have, oh, excuse me, I have 6x squared minus 1x squared, which is 5x squared. 17x minus 2x is a plus 15x, and then all I have left is a plus 5. This would be a perfectly acceptable answer, but many of you might recognize I can take out a GCF. I could divide out a 5 from all three of those terms. Oops. So if I took out a 5, I'd be left with x squared plus 3x plus 1. We will practice much more of that later on in the algebra unit. At this point, this would be a great answer. That would be the area of the shaded region of the picture.