Multiplying monomials to find area: two variables
About this video
Sal finds the area of a rectangle with length 4xy and width 2y. He multiplies the dimensions, regroups the factors, multiplies the coefficients and adds exponents on y to get the single-term answer 8xy^2.
You'll be able to
- write the area of a rectangle as the product of its length and width.
- multiply two monomials by multiplying coefficients and combining like variables.
- use y^1 times y^1 = y^2 by adding exponents with the same base.
Key words
- monomial
- An algebraic expression with just one term, like 8xy^2.
- area of a rectangle
- The product of its two dimensions: length times width.
- exponent
- The small number that tells how many times a base is multiplied by itself.
- coefficient
- The number multiplying the variables in a term, like the 8 in 8xy^2.
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.
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