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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 2, x or 7, y. 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.**

When a number is next to a variable, it means they are multiplied. So,

is the same as

left parenthesis, start color #11accd, minus, 4, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, x, squared, end color #ca337c, right parenthesis, left parenthesis, start color #11accd, 7, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, x, cubed, end color #ca337c, right parenthesis.

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).Then simplify, and we're done!

### Example 2

**Simplify.**

When a number is next to a variable, it means they are multiplied. So,

is the same as

left parenthesis, start color #11accd, minus, 8, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, a, squared, end color #ca337c, right parenthesis, left parenthesis, start color #11accd, minus, 5, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, a, start superscript, 6, end superscript, end color #ca337c, right parenthesis.

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).Then simplify, and we're done!

*Want to see another example? Check out this video.*

## Want to join the conversation?

- what to do if an expression is in the form of " (x^m)(y^(-k))(21 votes)
- 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(2 votes)
- 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.(2 votes)

- what is 2+2 in decimal form then put it as a polynomial(1 vote)
- 2.0 + 2.0

2x^0 + 2x^0(2 votes)

- 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?(0 votes)
- (6a2b)(−7a4b7) how would you solve this?(0 votes)
- 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(0 votes)

- Hi,

what is the answer for (-7X^2)^3(0 votes)- If something is raised to the power of 3, it means you need to multiply it with itself 3 times.

(-7X^2)^3 = (-7X^2) (-7X^2) (-7X^2) = (-7)(-7)(-7)(X^2*X^2*X^2) = -343x^6

Or, use the properties of exponents.

(-7X^2)^3 = (-7)^3 * x^(2*3) = -343x^6(2 votes)