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Sal expresses the area of a rectangle with length 4xy and width 2y as a monomial. Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
Express the area of a rectangle with length 4xy and width 2y as a monomial. Monomial just means just one term. So let's think about a rectangle. So let me draw a rectangle here. And they're telling us that the length is 4xy and they're telling us that the width is 2y. And just as a bit of a refresher, we know the area of a rectangle is just the width times the length, or the height times the width, or however you want to view it-- just the product of its two dimensions. So the area of this rectangle, the area is going to be equal to this length, 4xy times the width times 2y. We can simplify this. We have a 4 times a 2. Whenever you're just taking a product of a bunch of things you can switch the order however you like, as long as it's all multiplication. So 4 times 2, that gives us 8. Then we have this x sitting here. That is the only x we have there, so it's 8 times x. And then we have a y here. We could view that as y to the first. And then we have another y there. We could view that as y to the first. So y times y. You could view that as y squared. Or you could say look, y to the first times y to the first-- same base, add the two exponents-- 1 plus 1 is 2. So it's 8xy squared. This y squared covers both that y and that y over there. And we're done. We've expressed the area of this rectangle as a monomial.