Main content

### Course: Algebra (all content) > Unit 10

Lesson 4: Multiplying monomials# Multiplying monomials to find area

Learn to express the area of a rectangle with length 4y and width 2y as a monomial. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- What's monomial?(7 votes)
- what is the definition of a monomial(5 votes)
- A monomial is a number, a variable, or the product of a number and one or more variables with nonnegative integer exponents. it has only one term.(4 votes)

- Simplify (11k) to the second power(2 votes)
- (11k)^2 is made more simple is you write is as 11*11* then add the k*k which will simplify to 121K to the power of 2 also written as 121k^2. I hope this helps.(3 votes)

- I kind of don't understand why it would be y squared, because 1x1 is 1, so why is yxy y squared?(2 votes)
- Any number times itself = that number squared (or to the power of 2.

It just happens that 1^2 = 1 * 1 = 1

For most any other number, that relationship does not exist. For example: 3^2 = 3*3 = 9

Since we don't know the actual value of "y", we can't calculate "y * y". So, we write it in exponent form: "y^2".

Hope this helps.(2 votes)

- where are the practice problems for this section?(2 votes)
- There is not any, sorry. if you want to request that feature go to "Guidelines" > "request for features" at the bottom of the guidelines page(1 vote)

- Wait, so is 8 y^2 a polynomial or a monomial?(2 votes)
- Monomial. A monomial is an expression that is the product of constants and nonnegative integer powers of x, such as 5x^7. The coefficient--the number 5--is the constant term which is multiplying the variable term x. In your example, 8 is the coefficient and y is the variable term. Keep in mind, to be a monomial, the variable term needs to be raised to a positive power; if the exponent is negative or fractional, then the expression is not a monomial.(1 vote)

- So can you solve for the y? Or is it just left at the equation?(2 votes)
- I believe that it is just left at the equation. You can't solve the equation unless you're given a value for y. For example, if the problem in the video said that y = 3, then we can substitute y for 3 and then solve, but we can't solve for y. Thanks for asking that. Hope this helps.(1 vote)

- pls help me:

What is a monomial? i still don't get it...HELP!(1 vote)- It is a polynomial with only 1 term. Example: 3x^2, 2x, 3.56794735y. Anything with only 1 term.(2 votes)

- i Don't understand any of this. Please Explain to me.(1 vote)
- is there an adding and subtracting monomials. i really need that(1 vote)

- Is there an introduction to monomials, and polynomials?(2 votes)
- As Aileen was saying in the video, a monomial is a polynomial with only one term. Remember that a term can be like a number and an exponent, such as 5^2, a number with a variable, such as 3y, or both, such as 3y^2. Basically a term is a single number either by itself or with a variable, an exponent, or both. In the problem in the video, the monomial is 8y^2. Hope this helps you.(1 vote)

## Video transcript

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.