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.

Hi, what is the answer for (-7X^2)^3

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

Main content

Algebra (all content)

Course: Algebra (all content) > Unit 10

Lesson 4: Multiplying monomials

Multiplying monomials review

CCSS.Math:

HSA.APR.A.1

Google Classroom

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.

left parenthesis, minus, 4, x, squared, right parenthesis, left parenthesis, 7, x, cubed, right parenthesis

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

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

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).

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

Then simplify, and we're done!

start color #11accd, minus, 28, end color #11accd, start color #ca337c, x, start superscript, 5, end superscript, end color #ca337c

Example 2

Simplify.

left parenthesis, minus, 8, a, squared, right parenthesis, left parenthesis, minus, 5, a, start superscript, 6, end superscript, right parenthesis

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

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

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).

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

Then simplify, and we're done!

start color #11accd, 40, end color #11accd, start color #ca337c, a, start superscript, 8, end superscript, end color #ca337c

Want to see another example? Check out this video.

Practice

Problem 1

Current

Simplify.

left parenthesis, 7, h, cubed, right parenthesis, left parenthesis, 3, h, start superscript, 7, end superscript, right parenthesis

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

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Ashutosh kumar
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what to do if an expression is in the form of " (x^m)(y^(-k))
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- Candace Dyck
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  You would put down xy^m-k, but you can't simplify it anymore than that, without any numbers.
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Melissa
Posted 5 years ago. Direct link to Melissa's post “How do you solve as probl...”
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
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(2 votes)
Answer
- Aiena
  Posted 4 years ago. Direct link to Aiena's post “Hi Melissa, You're on th...”
  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.
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Wirt, Alexander
Posted 4 years ago. Direct link to Wirt, Alexander's post “what is 2+2 in decimal fo...”
what is 2+2 in decimal form then put it as a polynomial
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- Ziggletooth
  Posted 4 years ago. Direct link to Ziggletooth's post “2.0 + 2.0 2x^0 + 2x^0”
  2.0 + 2.0
  2x^0 + 2x^0
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st25ericey
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what do you do if there is a negative variable squared and no number?
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Tulsi Patel
Posted 5 years ago. Direct link to Tulsi Patel's post “How can a variable not be...”
How can a variable not be in the denominator in a monomial?
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nassir dickson
Posted 5 years ago. Direct link to nassir dickson's post “(6a2b)(−7a4b7) how would ...”
(6a2b)(−7a4b7) how would you solve this?
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- Nicolas Retamar
  Posted 5 years ago. Direct link to Nicolas Retamar's post “To solve this, you should...”
  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
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kartik123
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Hi,
what is the answer for (-7X^2)^3
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- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “If something is raised to...”
  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
  Comment on Kim Seidel's post “If something is raised to...”
  (2 votes)