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# Multiplying monomials to find area: two variables

CCSS Math: HSA.APR.A.1, HSA.SSE.A.1

## 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.