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Studying for a test? Prepare with these 9 lessons on Polynomials.
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Express the area of a rectangle with the length 4y and width 2y as a monomial. So the area of a rectangle is just the width times the height, or the base times the height. Now here, the base is 4y. So let me just write it down-- area is going to be equal to the width of the base times the height. The width is 4y and the height here is 2y. So the area is going to be 4y times 2y. Now here we can just use the associative and the commutative properties of multiplication. So just swap the order that we do this multiplying in. Instead of multiplying 4 times y times 2 times y, we could say this is the same thing as 4 times 2 times y times y. And of course, 4 times 2, that part right over there is just equal to 8. And then y times y, well that's just y squared. Or it's y to the first times y to the first, which is also y squared. So it becomes 8y squared. So that's the area and it's a monomial. This is a polynomial with only one term.