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CCSS.Math: ,

express the area of a rectangle with length for X Y and with 2y as a monomial monomial just means just one term monomial so let's think about a rectangle so let me draw a rectangle here let me draw a rectangle and they're telling us that the length is 4 X Y the length is 4 X Y and they're telling us that the width is 2 y the width is 2i and just as a bit of refresher we know the area of a rectangle is just the width times the length or 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 for XY is going to be equal to 4 X Y 4 XY times the width times the width times 2y times 2y and we can simplify this we have a 4 times a 2 we have a 4 times - 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 can 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 the first times y to the first same base add the two exponents 1 plus 1 is 2 so it's 8 X Y squared this cook 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