Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to multiply polynomials

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 Polynomials

Expand:

$3x^{2}y\left ( 4x^{3}y-9x^{2}y^{2}+xy-10 \right )$

Possible Answers:

$12x^{4}y-27x^{3}y^{2}+3x^{2}y-30x^{2}y$

$12x^{4}y^{2}-27x^{3}y^{3}+3x^{2}y^{2}-30xy$

$12x^{5}y-27x^{4}y^{2}+3x^{3}y-30x^{2}y$

$12x^{5}y^{2}-27x^{3}y^{3} + 3x^{3}y^{2}-30xy$

$12x^{5}y^{2}-27x^{4}y^{3}+3x^{3}y^{2}-30x^{2}y$

Correct answer:

$12x^{5}y^{2}-27x^{4}y^{3}+3x^{3}y^{2}-30x^{2}y$

Explanation:

Distribute $3x^{2}y$ through every term in the parentheses.

This gives us the following:

$12x^{5}y^{2}-27x^{4}y^{3}+3x^{3}y^{2}-30x^{2}y$

Report an Error

Example Question #1 : How To Multiply Polynomials

Multiply:

$( 3x^{2}-2x+5 )\cdot ( - x^{3}+2x^{2}-5x-10 )$

Possible Answers:

$-3x^{4}+8x^{3}-24x^{2}-10x-55$

$-3x^{5}-8x^{4}+24x^{3}+10x^{2}+5x+50$

$3x^{4}+8x^{3}-24x^{2}-15x-50$

$-3x^{5}+8x^{4}-24x^{3}-10x^{2}-5x-50$

$-3x^{5}+4x^{4}-16x^{3}-4-30x^{2}-45x+50$

Correct answer:

$-3x^{5}+8x^{4}-24x^{3}-10x^{2}-5x-50$

Explanation:

First multiply each of the terms inside the second parentheses by $3x^{2}$ :

$-3x^{5}+6x^{4}-15x^{3}-30x^{2}$

Next multiply each of the terms inside the second parentheses by -2x :

$2x^{4}-4x^{3}+10x^{2}+20x$

Finally multiply each of the terms inside the second parentheses by 5:

$-5x^{3}+10x^{2}-25x-50$

By combining all like terms we get the correct answer:

$-3x^{5}+8x^{4}-24x^{3}-10x^{2}-5x-50$

Report an Error

Example Question #91 : Variables

Expand:

(x + 3)(x^2 - 2x + 5)

Possible Answers:

x^3 + x^2 + x + 15

x^3 - x^2 - x + 15

x^3 + 5x^2 - x + 15

x^3 + x^2 - x - 15

x^3 + x^2 - x + 15

Correct answer:

x^3 + x^2 - x + 15

Explanation:

The first step is to distribute the first term in the binomial across the trinomial:

x(x^2 - 2x + 5) = x^3 - 2x^2 + 5x

Then multiply the second term in the binomial across the same trinomial:

3(x^2 - 2x + 5) = 3x^2 - 6x + 15

You can then combine like terms to reach a simplified answer:

(x+3)(x^2 - 2x + 5) = x^3 - 2x^2 + 5x + 3x^2 - 6x + 15

=x^3 - 2x^2 + 5x + 3x^2 - 6x + 15

=x^3 + x^2 - x + 15

Report an Error

Example Question #91 : Polynomials

Multiply the expression: (x^2 + y^2) (2x - 4)

Possible Answers:

x^3-4 x^2+2 x y^2- y^2

2 x^3-4 x^2+2 x y^2-4 y^2

2 x^3-4 x^2+2 x^2 y^2-4 y

2 x^2-4 x+2 x y^2-4 y^2

2 x^3-4 x^2 + y^2

Correct answer:

2 x^3-4 x^2+2 x y^2-4 y^2

Explanation:

When we FOIL this expression, we start by multiplying the first term of the first binomial with the first term of the second binomial. Then we multiply the two "outside" terms (in this case those are x^2 and 4). Next we multiply the "inside" terms (in this case the two inside terms are y^2 and ) and finally the last terms.

When we combine terms in this way, it is important to make sure we are paying attention to the exponents! We want to add the exponents when we multiply terms. So, when multiplying $(x^2)\cdot (x)$ , we want to add the 2 with 1 (the exponent of an un-powered variable is always 1!) and we get 3! So we know the resulting power would be 3, like this: x^3

Using that skill and the FOIL technique, we end up with the answer, 2 x^3-4 x^2+2 x y^2-4 y^2

Report an Error

Example Question #5 : How To Multiply Polynomials

Expand: (2x + 6) (5x^2 - 5)

Possible Answers:

10 x^2+30 x-30

x^3+30 x^2- x-30

10 x^3+30 x^2 +10 x+30

10 x^3+30 x^2-10 x-30

10 x^3+30 x^2-10 x

Correct answer:

10 x^3+30 x^2-10 x-30

Explanation:

When we FOIL this expression, we start by multiplying the first term of the first binomial with the first term of the second binomial. Then we multiply the two "outside" terms (in this case those are the and ). Next we multiply the "inside" terms (in this case the two inside terms are and 5x^2 ) and finally the last terms.

When we combine terms in this way, it is important to make sure we are paying attention to the exponents! When we multiply like terms with exponents, we can add the exponents together! In this case, we have an (which since it has no power, means it is to the power of 1) and an x^2 . We can add these exponents together when we go through our FOIL process and get . So we know the resulting power would be , like this: x^3

Using that skill and the FOIL technique, we end up with the answer:

10 x^3+30 x^2-10 x-30

Report an Error

Example Question #1 : Simplifying Polynomials

Multiply:

$\left (x^{2} + 2x + 7 \right ) \left (x^{2} + x - 6 \right )$

Possible Answers:

$x^{4} + 3 x^{3} -x^{2} - 5x - 42$

$x^{4} + 3 x^{3} -15x^{2} - 19x - 42$

$x^{4} + 3 x^{3} + 19x^{2} - 5x - 42$

$x^{4} + 3 x^{3} +3x^{2} - 5x - 42$

$x^{4} + 3 x^{3} -x^{2} - 19x - 42$

Correct answer:

$x^{4} + 3 x^{3} +3x^{2} - 5x - 42$

Explanation:

$\left (x^{2} + 2x + 7 \right ) \left (x^{2} + x - 6 \right )$

$= x^{2}\left (x^{2} + x - 6 \right ) + 2x \left (x^{2} + x - 6 \right ) + 7 \left (x^{2} + x - 6 \right )$

$= x^{2} \cdot x^{2} + x^{2} \cdot x - x^{2} \cdot 6 + 2x \cdot x^{2} + 2x \cdot x - 2x \cdot 6 + 7 \cdot x^{2} + 7 \cdot x - 7 \cdot 6$

$= x^{4} + x^{3} - 6x^{2} + 2x^{3} + 2x^{2} - 12x + 7x^{2} +7x - 42$

$= x^{4} + x^{3} + 2x^{3} - 6x^{2} + 2x^{2} + 7x^{2} - 12x +7x - 42$

$= x^{4} + 3 x^{3} +3x^{2} - 5x - 42$

Report an Error

Example Question #1 : Simplifying Polynomials

Simplify the expression.

$\small (3x+2)-(x+4)(x+1)$

Possible Answers:

$\small -x^2-8x-6$

$\small -x^2-2x-2$

$\small x^2+8x+6$

$\small -x^2+8x+6$

Correct answer:

$\small -x^2-2x-2$

Explanation:

$\small (3x+2)-(x+4)(x+1)$

Use FOIL to expand the monomials.

(x+4)(x+1)

x^2+x+4x+4=x^2+5x+4

Return this expansion to the original expression.

$\small (3x+2)-(x^2+5x+4)$

Distribute negative sign.

$\small (3x+2)-x^2-5x-4$

Combine like terms.

$\small -x^2+3x-5x+2-4$

$\small -x^2-2x-2$

Report an Error

Example Question #1 : How To Multiply Polynomials

Simplify the expression.

$x^{5}*x^{16}$

Possible Answers:

The expression cannot be simplified further.

$x^{21}$

$x^{80}$

$x^{11}$

$2x^{16}$

Correct answer:

$x^{21}$

Explanation:

When multiplying exponential components, you must add the powers of each term together.

5+16=21

$x^{5}*x^{16}=x^{21}$

Report an Error

Example Question #91 : Polynomials

$x^{5}y^{17}*x^{2}y^{2}=?$

Possible Answers:

$x^{7}y^{19}$

None of the other answers are correct.

$2x^{2}x^{7}y^{19}$

$x^{2}y^{8}$

$x^{10}y^{34}$

Correct answer:

$x^{7}y^{19}$

Explanation:

When multiplying polynomials, add the powers of each like-termed variable together.

For x: 5 + 2 = 7

For y: 17 + 2 = 19

Therefore the answer is $x^{7}y^{19}$ .

Report an Error

Example Question #2 : Simplifying And Expanding Quadratics

Multiply: $(x^{2} + 3) (4x - 1)$

Possible Answers:

$4x^{3} +x^{2} -12x - 3$

$4x^{3} + 3$

$4x^{3} -x^{2} +12x - 3$

$4x^{3} - 3$

$4x^{3} -x^{2} -12x + 3$

Correct answer:

$4x^{3} -x^{2} +12x - 3$

Explanation:

$(x^{2} + 3) (4x - 1)$

$= x^{2} (4x - 1) + 3(4x - 1)$

$= x^{2} \cdot 4x - x^{2} \cdot 1 + 3 \cdot 4x - 3 \cdot 1$

$= 4x^{3} - x^{2} + 12x - 3$

Report an Error

View Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra Tutors

Arianna
Certified Tutor

Washington State University, Bachelor in Arts, Communication, General. City University of Seattle, Masters in Business Admini...

View Algebra Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

All Algebra 1 Resources

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

Popular Subjects

Calculus Tutors in Seattle, LSAT Tutors in Washington DC, ISEE Tutors in Phoenix, English Tutors in Dallas Fort Worth, GRE Tutors in Miami, Computer Science Tutors in Boston, Spanish Tutors in Dallas Fort Worth, Reading Tutors in Washington DC, French Tutors in Miami, English Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Chicago, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Boston, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Boston, GMAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles

Popular Test Prep

GRE Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Washington DC, ISEE Test Prep in San Diego, ISEE Test Prep in Boston, SSAT Test Prep in Phoenix, ACT Test Prep in Los Angeles, GMAT Test Prep in Dallas Fort Worth, GRE 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

Algebra 1 : How to multiply polynomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Multiply Polynomials

Example Question #1 : How To Multiply Polynomials

Example Question #91 : Variables

Example Question #91 : Polynomials

Example Question #5 : How To Multiply Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : How To Multiply Polynomials

Example Question #91 : Polynomials

Example Question #2 : Simplifying And Expanding Quadratics

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: