Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Monomials

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : Algebra

If you have a rectangle with a width of $\displaystyle 3n$ and a length of $\displaystyle 7n-3y +2$ , what is the area of the rectangle?

Possible Answers:

$56n^{2}-27ny+18n$ $\displaystyle 56n^{2}-27ny+18n$

$21n-9y^{2}+6$ $\displaystyle 21n-9y^{2}+6$

$\displaystyle 21ny-9ny+2ny$

$21n^{2}-9ny+6n$ $\displaystyle 21n^{2}-9ny+6n$

$14ny^{3}$ $\displaystyle 14ny^{3}$

Correct answer:

$21n^{2}-9ny+6n$ $\displaystyle 21n^{2}-9ny+6n$

Explanation:

To find the area of a rectangle, multiply the length times the width. Therefore, you must multiply $\displaystyle 3n$ times $\displaystyle 7n-3y +2$ . To do that, you must multiply the monomial times each part of the trinomial, like so:

$\displaystyle 7n(3n)-3y(3n) +2(3n)$

$\displaystyle 21n^2-9ny+6n$

Report an Error

Example Question #722 : Psat Mathematics

Find the product:

$\displaystyle 6x^3y^5(3x^2z^4+x^3y+7y)$

Possible Answers:

$\displaystyle 9x^5y^6+6x^3y^6+7$

$\displaystyle 1$

$\displaystyle 18x^6y^5z^4+6x^9y^5+42x^3y^5$

$\displaystyle 6x^3y^5z^4+6x^3y^5+7y^6$

$\displaystyle 18x^5y^5z^4 + 6x^6y^6+42x^3y^6$

Correct answer:

$\displaystyle 18x^5y^5z^4 + 6x^6y^6+42x^3y^6$

Explanation:

Use the distributive property:

$\displaystyle 6x^3y^5(3x^2z^4+x^3y+7y)$

$\displaystyle (6x^3y^5)(3x^2z^4)+(6x^3y^5)(x^3y)+(6x^3y^5)(7y)$

Simplify: don't forget to use the rules of multiplying exponents (add them)

$\displaystyle 18x^5y^5z^4 + 6x^6y^6+42x^3y^6$

Report an Error

Example Question #723 : Psat Mathematics

Find the product:

$\displaystyle 4a^2(ab^2+a^2b+ac^3)$

Possible Answers:

$\displaystyle 4a^3b^2+4a^4b+4a^3b^3$

$\displaystyle 4ab^3+4a^2b^3+4ac$

$\displaystyle 4a^2b^3+4ab$

$\displaystyle 8a^2b^2+4a^4b$

$\displaystyle 4a^2b^2+4a^4b+4a^2b^3$

Correct answer:

$\displaystyle 4a^3b^2+4a^4b+4a^3b^3$

Explanation:

Find the product:

$\displaystyle 4a^2(ab^2+a^2b+ac^3)$

Use the distributive property:

$(4a^2\cdot ab^2)+(4a^2\cdot a^2b)+(4a^2\cdot ac^3)$ $\displaystyle (4a^2\cdot ab^2)+(4a^2\cdot a^2b)+(4a^2\cdot ac^3)$

When multiplying variables with exponents, add the exponents:

$\displaystyle 4a^3b^2+4a^4b+4a^3c^3$

Report an Error

Example Question #3 : Monomials

Find the product:

$\displaystyle 5x^3(x^2+2x+4)$

Possible Answers:

$\displaystyle 5x^5+10x^4+20x^3$

$\displaystyle 5x^6+30x^3$

$\displaystyle 5x^2+2.5x^2+1.25x^3$

$\displaystyle 5x^6+10x^4+20x^3$

$\displaystyle 5x^3+x^2+2x+4$

Correct answer:

$\displaystyle 5x^5+10x^4+20x^3$

Explanation:

Find the product:

$\displaystyle 5x^3(x^2+2x+4)$

Use the distributive property:

$(5x^3 \cdot x^2)+(5x^3 \cdot 2x)+(5x^3 \cdot 4)$ $\displaystyle (5x^3 \cdot x^2)+(5x^3 \cdot 2x)+(5x^3 \cdot 4)$

$\displaystyle 5x^5+10x^4+20x^3$

Report an Error

View PSAT Mathematics Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, Bachelor of Science, Mathematics.

View PSAT Mathematics Tutors

Zachary
Certified Tutor

Yale University, Bachelor of Science, Biology, General.

View PSAT Mathematics Tutors

Zachary
Certified Tutor

University of South Florida-Main Campus, Bachelor of Education, High School Teaching. University of South Florida-Main Campus...

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Seattle, GRE Tutors in Dallas Fort Worth, ISEE Tutors in Seattle, ACT Tutors in Phoenix, Physics Tutors in Denver, Algebra Tutors in Philadelphia, GRE Tutors in San Diego, Biology Tutors in Dallas Fort Worth, LSAT Tutors in Boston, Statistics Tutors in Dallas Fort Worth

Popular Courses & Classes

GMAT Courses & Classes in Atlanta, SAT Courses & Classes in Chicago, ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in New York City, GMAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Miami, MCAT Courses & Classes in Seattle, ISEE Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in New York City, MCAT Test Prep in Washington DC, MCAT Test Prep in New York City, ISEE Test Prep in Boston, GMAT Test Prep in Chicago, ISEE Test Prep in Phoenix, LSAT Test Prep in Philadelphia, GRE Test Prep in Dallas Fort Worth, GMAT Test Prep in Philadelphia, SSAT Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

PSAT Math : Monomials

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #71 : Algebra

Example Question #722 : Psat Mathematics

Example Question #723 : Psat Mathematics

Example Question #3 : Monomials

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: