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Course: Algebra (all content) > Unit 10
Lesson 4: Multiplying monomialsMultiplying 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)