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## Algebra (all content)

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

Lesson 4: Multiplying monomials

# Multiplying monomials review

A monomial is a polynomial with just one term. For example, 2a^5 is a monomial. This article reviews how to multiply monomials (e.g., 2a^5 * 3a^2 = 6a^7).
A monomial is a polynomial with just one term, like $2x$ or $7y$. Multiplying monomials is a foundational skill for being able to multiply binomials and polynomials more generally, so it's good to review a few examples.

### Example 1

Simplify.
$\left(-4{x}^{2}\right)\left(7{x}^{3}\right)$
When a number is next to a variable, it means they are multiplied. So,
$\left(-4{x}^{2}\right)\left(7{x}^{3}\right)$
is the same as
$\left(-4\right)\left({x}^{2}\right)\left(7\right)\left({x}^{3}\right)$.
Now we can rearrange the factors because multiplication is commutative (a fancy way of saying that the order in which we multiply things doesn't matter).
$\left(-4\right)\left(7\right)\left({x}^{2}\right)\left({x}^{3}\right)$
Then simplify, and we're done!
$-28{x}^{5}$

### Example 2

Simplify.
$\left(-8{a}^{2}\right)\left(-5{a}^{6}\right)$
When a number is next to a variable, it means they are multiplied. So,
$\left(-8{a}^{2}\right)\left(-5{a}^{6}\right)$
is the same as
$\left(-8\right)\left({a}^{2}\right)\left(-5\right)\left({a}^{6}\right)$.
Now we can rearrange the factors because multiplication is commutative (a fancy way of saying that the order in which we multiply things doesn't matter).
$\left(-8\right)\left(-5\right)\left({a}^{2}\right)\left({a}^{6}\right)$
Then simplify, and we're done!
$40{a}^{8}$
Want to see another example? Check out this video.

## Practice

Problem 1
Simplify.
$\left(7{h}^{3}\right)\left(3{h}^{7}\right)$

Want more practice? Check out this exercise. Also check out this challenge exercise.

## Want to join the conversation?

• what to do if an expression is in the form of " (x^m)(y^(-k))
• You would put down xy^m-k, but you can't simplify it anymore than that, without any numbers.
(1 vote)
• How do you solve as problem like: a rectangle has a length (l) of 1 1/3xyz and a width (w) of 15z/y. given that Area=l*w, find the area of the rectangle? i know it would look like 1 1/3xyz * 15 z/y=A but i dont know how to solve it from there
• Hi Melissa,

You're on the right track! So, the area of a rectangle is length * breath.

Area = 11/3xyz * 15z/y
= (11*15z)/ (3xyz * y) (putting all terms in the numerator and denominator)
= 55/xyˆ2 (canceled the "z" in the numerator and denominator, divided 15 by 3, multiplied 11 by 5 and y*y is yˆ2)

Hence, the area of the rectangle is 55/xyˆ2.

I hope this helped.

Aiena.
• what is 2+2 in decimal form then put it as a polynomial
(1 vote)
• 2.0 + 2.0
2x^0 + 2x^0
• what do you do if there is a negative variable squared and no number?
(1 vote)
• How can a variable not be in the denominator in a monomial?
• (6a2b)(−7a4b7) how would you solve this?
• To solve this, you should multiply the coefficients first, and multiply the variables next
6*-7= -42, and (x^2 * x^4) = x^2+4= x^6, and b^1 * b^7= b^8
last step: combine
-42x6b8