We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Multiply A Monomial By A Polynomial

$Expand \;x(x-2)$

Possible Answers:

$x^{2}+2x$

2x -2

$x^{2}$

$x^{2}-2x$

Correct answer:

$x^{2}-2x$

Explanation:

Report an Error

Example Question #1 : Monomials

Evaluate.

$ab(ab^{2}+4a-b)$

Possible Answers:

$a^{2}b^{3}+4a^{2}b-ab^{2}$

$4a^{3}b^{2}$

2ab+4a-b

$a^{2}b^{2}+4a-b$

Correct answer:

$a^{2}b^{3}+4a^{2}b-ab^{2}$

Explanation:

$ab(ab^{2}+4a-b)$

Using the distributive property you are simply going to share the term , with every term in the poynomial

$ab\cdot ab^{2}+ ab\cdot 4a- ab\cdot b$

Now because we are multiplying like variables we can add the exponents, to simplify each expression

$a^{2}b^{3}+4a^{2}b-ab^{2}$

This will be our final answer because we can not add terms unless they are 'like' meaning they contain the same elements and degrees.

Report an Error

Example Question #1 : How To Multiply A Monomial By A Polynomial

Multiply:

$-3t ^{2} ( 2t ^{2} - 5t + 7)$

Possible Answers:

$-6 t ^{4} - 15t ^{3} +21t ^{2}$

$-6 t ^{4} + 5t ^{3} -7t ^{2}$

$-6 t ^{4} - 5t ^{3} +7t ^{2}$

$-6 t ^{4} + 15t ^{3} -21t ^{2}$

$-6 t ^{4} - 15t ^{3} -21t ^{2}$

Correct answer:

$-6 t ^{4} + 15t ^{3} -21t ^{2}$

Explanation:

$-3t ^{2} ( 2t ^{2} - 5t + 7)$

$= -3t ^{2} \cdot 2t ^{2} - \left (-3t ^{2} \right )\cdot 5t +\left (-3t ^{2} \right )\cdot 7$

$= -3t ^{2} \cdot 2t ^{2} + 3t ^{2} \cdot 5t -3t ^{2}\cdot 7$

$= -3\cdot 2 \cdot t ^{2} \cdot t ^{2} + 3\cdot 5 \cdot t ^{2} \cdot t -3\cdot 7 \cdot t ^{2}$

$= -6 \cdot t ^{2+2} + 15\cdot t ^{2+1} -21 \cdot t ^{2}$

$= -6 t ^{4} + 15t ^{3} -21t ^{2}$

Report an Error

Example Question #1 : Monomials

Simplify the following:

$(2p^{2})(4x+p)$

Possible Answers:

$(8xp)^{2}+2p^{3}$

$8xp^{2}+2p^{2}$

None of the other answers

$6xp^{2}+3p^{3}$

$8xp^{2}+2p^{3}$

Correct answer:

$8xp^{2}+2p^{3}$

Explanation:

Distribute the $2p^{2}$ to each term in the parentheses in the other polynomial.

$2p^{2}(4x)=8xp^{2}$

$2p^{2}(p)=2p^{3}$

Putting the results back together

$(2p^{2})(4x+p)=8xp^{2}+2p^{3}$

Report an Error

Example Question #4 : Monomials

Multiply:

-4x(3x^2-2x+4)

Possible Answers:

12x^3-8x^2+16x

-12x^3+8x^2-16x

-12x^3-8x^2-16x

-12x^3-8x^2+16x

Correct answer:

-12x^3+8x^2-16x

Explanation:

Multiply each term of the polynomial by -4x . Be careful to distribute the negative sign.

(-4x)(3x^2)=-12x^3

(-4x)(-2x)=8x^2

(-4x)(4)=-16x

Add the individual terms together:

-12x^3+8x^2+(-16x)=12x^3+8x^2-16x

Report an Error

Example Question #3 : Monomials

Simplify the following

$(7y)(7t-3y^{3} + 2)$

Possible Answers:

$49yt-21y^{2} +14y$

$14yt-21y^{4} +14y$

$14yt-10y^{4} +14y$

$49yt-21y^{4} +14y$

$28y-21y^{4} +14t$

Correct answer:

$49yt-21y^{4} +14y$

Explanation:

Distribute to each term in the parentheses in the polynomial

7y(7t)=49yt

$7y(-3y^{3})=-21y^{4}$

7y(2)=14y

Combine the results

$(7y)(7t-3y^{3} + 2)=49yt-21y^{4} +14y$

Report an Error

Example Question #2 : Monomials

Expand the expression by multiplying the terms.

$\small (x-4)(x+2)(2x-5)$

Possible Answers:

$\small 2x^3-9x^2-6x+40$

$\small 2x^3-x^2-26x+40$

$\small 2x^3+9x^2-6x+40$

$\small 2x^3+x^2-26x+40$

Correct answer:

$\small 2x^3-9x^2-6x+40$

Explanation:

$\small (x-4)(x+2)(2x-5)$

When multiplying, the order in which you multiply does not matter. Let's start with the first two monomials.

(x-4)(x+2)

Use FOIL to expand.

x^2+2x-4x-8=x^2-2x-8

Now we need to multiply the third monomial.

$\small (x-4)(x+2)(2x-5)=(x^2-2x-8)(2x-5)$

Similar to FOIL, we need to multiply each combination of terms.

2x(x^2-2x-8)+(-5)(x^2-2x-8)

2x^3-4x^2-16x-5x^2+10x+40

Combine like terms.

2x^3-9x^2-6x+40

Report an Error

Example Question #1 : Monomials

Find the product:

$\small 7n(8n-2)$

Possible Answers:

$\small 56n^2-14n$

$\small n-14$

$\small n^2-14n$

$\small n^2+14$

Correct answer:

$\small 56n^2-14n$

Explanation:

First, mulitply the mononomial by the first term of the polynomial:

$\small 7n\times8n\ = 56n^2$

Second, multiply the monomial by the second term of the polynomial:

$\small 7n\times (-2)\ = -14n$

Add the terms together:

$\small 56n^2\ +\ (-14n)\ = 56n^2-14n$

Report an Error

Example Question #3 : Simplifying Expressions

Expand: 8x(3x+7)

Possible Answers:

11x^2 + 15x

11x + 15

24x^2 + 56

24x + 56

24x^2 + 56x

Correct answer:

24x^2 + 56x

Explanation:

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

Report an Error

Example Question #1 : How To Multiply A Monomial By A Polynomial

Write 4x^2(3x^2+2x+4) as a polynomial.

Possible Answers:

$12x^{4}+8x^{2}+8x$

$7x^{4}+6x^{3}+8x^{2}$

$12x^{4}+8x^{3}+16x^{2}$

$12x^{2}+8x+16$

$36x^{2}$

Correct answer:

$12x^{4}+8x^{3}+16x^{2}$

Explanation:

We need to distribute the 4x² through the terms in the parentheses:

4x^2(3x^2+2x+4)=4x^2(3x^2)+4x^2(2x)+4x^2(4)

This becomes 12x^4+8x^3+16x^2 .

Report an Error

View Algebra Tutors

Armon
Certified Tutor

Loyola University-Chicago, Bachelor of Science, Biology, General. Columbia College-Chicago, Bachelor of Science, Graphic Desi...

View Algebra Tutors

Karine
Certified Tutor

University of California-San Diego, Bachelor of Science, Political Science and Government. University of Southern California,...

View Algebra Tutors

Ivonne
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Chemistry.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in San Francisco-Bay Area, French Tutors in Seattle, Math Tutors in Houston, GMAT Tutors in Philadelphia, French Tutors in Boston, Physics Tutors in Phoenix, Statistics Tutors in Seattle, Spanish Tutors in San Francisco-Bay Area, Reading Tutors in Dallas Fort Worth, GMAT Tutors in Houston

Popular Courses & Classes

ACT Courses & Classes in Boston, MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Seattle, GRE Courses & Classes in San Diego, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Diego, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in New York City, LSAT Test Prep in San Diego, SSAT Test Prep in Chicago, ACT Test Prep in Boston, GRE Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Chicago, ACT Test Prep in Miami, SAT Test Prep in Seattle, ISEE Test Prep in Houston

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

Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Multiply A Monomial By A Polynomial

Example Question #1 : Monomials

Example Question #1 : How To Multiply A Monomial By A Polynomial

Example Question #1 : Monomials

Example Question #4 : Monomials

Example Question #3 : Monomials

Example Question #2 : Monomials

Example Question #1 : Monomials

Example Question #3 : Simplifying Expressions

Example Question #1 : How To Multiply A Monomial By A Polynomial

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: