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Algebra (all content)
Course: Algebra (all content)ย >ย Unit 10
Lesson 4: Multiplying monomialsMultiplying monomials to find area: two variables
CCSS.Math: ,
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.
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So if you have an exponent in a term like this with more than one variable, does the exponent act on just the variable it's next to (in this case y) or the whole term? It seems from this like it's the whole term, but that doesn't seem intuitive as there's only one x in the original terms...(6 votes)
An exponent just acts on the thing it is next to. So if you have 2xy^2 then it is only the y which is squared. If you wanted the x squared as well you would have to explicitly write 2 x^2 y^2, or use brackets so that the exponent acts on everything inside the brackets: 2(xy)^2.(6 votes)
- can a coefficient number be negative(3 votes)
I can see at0:57that you have put a video of multiplying monomials, but I wanted a video of dividing monomials. Is there such a video somewhere on this website?(2 votes)
same here specifically dividing monomials by binomials(1 vote)
- Is there a video explaining what polynomials, monomials, and binomials are?(1 vote)
Those are covered in the intro to polynomials section: https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/introduction-to-polynomials/v/polynomials-intro(3 votes)
- Can't the area also be founds by adding 4xy+4xy+2y+2y, which = 8xy+4y? Can someone show me how this is = to 8xy^2? Thanks(1 vote)
- Area = Length * Width
You are finding the perimeter = 2(length) + 2(width).
They are not the same.(2 votes)
Is there a video that helps with binomials,monomials,polynomials?(1 vote)
There's an entire set of videos https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions , without a more specific question it's going to be hard to give a more specific answer...(2 votes)
- How do u multiply and divide -48y3 and -8y?(2 votes)
- If you mean -48y cubed, you should type it like this: -48y^3. And multiplying it is simple, -8y is just like saying -8y^1. So really, you are just adding the exponents, 1 and 3 to get four. And 48 times 8 is equal to 384. So when you multiply it, the answer is 384y^4. To divide, you just subtract 1 from 3, and divide 48 by 8 to get 6y^2. Hope this helped.(0 votes)
What exactly is the term that is both behind 4 and 2?(0 votes)- They are not terms but factors (something you multiply with).
You use letters instead of numbers to indicate that it is a variable. The value of x and y could be any number (in this case they should be positive since sidelengths are positive)(3 votes)
- How do I get rid of negative exponenants in dividing monomials(1 vote)
- Negative exponents, remember, mean 1/whatever the rest is. You can "flip" the expression to the other part of the fraction and make it a positive exponent.(1 vote)
- How do u divide the monomials if it has negative exponents(1 vote)
- When you have negative exponents, it is the same thing as its reciprocal(or as I like to call it, flipping it). When you divide your exponents, you subtract (to be specific, you subtract the divisor's [bottom one] exponent from the dividend's [top one] exponent. Just say if you don't understand, okay?(1 vote)
0:57Video 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.