We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Distributive Property

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 Use Foil In The Distributive Property

What is the equation that has the following solutions? x=5,-8

Possible Answers:

$x^{2}-3x+40$

$x^{2}+3x-40$

$x^{2}+5x-60$

$x^{2}+13x-40$

Correct answer:

$x^{2}+3x-40$

Explanation:

This is a FOIL-ing problem. First, set up the numbers in a form we can use to create the function.

Take the opposite sign of each of the numbers and place them in this format. (x-5)(x+8)

Multiply the in the first parentheses by the and 8 in the second parentheses respectively to get $x^{2}+8x$

Multiply the in the first parentheses by the and 8 in the second parentheses as well to give us -5x-40 .

Then add them together to get $x^{2}+8x-5x-40$

Combine like terms to find the answer which is $x^{2}+3x-40$ .

Report an Error

Example Question #2 : How To Use Foil In The Distributive Property

Simplify the following expression.

$(3x^{2}-3)(2x^{3}-8)$

Possible Answers:

$6x^{5}-30x^{2}-24$

$6x^{5}-6x^{3}-24x^{2}+24$

$6x^{6}-6x^{3}-24x^{2}+24$

$6x^{5}-30x^{2}+24$

$6x^{5}-6x^{3}-24x^{2}-24$

Correct answer:

$6x^{5}-6x^{3}-24x^{2}+24$

Explanation:

Simplify using FOIL method.

Remember that multiplying variables means adding their exponents.

F: $3x^{2}*2x^{3} = 6x^{5}$

O: $3x^{2}*(-8) = -24x^{2}$

I: $-3 *2x^{3}=-6x^{3}$

L: -3 *-8= 24

Combine the terms. Note that we cannot simplify further, as the exponents do not match and cannot be combined.

$6x^{5}-6x^{3}-24x^{2}+24$

Report an Error

Example Question #3 : How To Use Foil In The Distributive Property

$\left ( 3x+2\right )\left ( 2x-5\right )=$

Possible Answers:

$6x^{2}+19x -10$

$6x^{2}-3x-10$

$6x^{2}+19x+10$

$6x^{2}-11x-10$

$6x^{2}+2x-3$

Correct answer:

$6x^{2}-11x-10$

Explanation:

$\textup{FOIL: Product is the sum of the products of the first, outer, inner and last terms:}$

$\left ( 3x+2\right )\left ( 2x-5\right )=$ $3x\ast2x+3x\left ( -5\right )+ 2\ast2x+2\left ( -5\right )$

$6x^{2}-15x+4x-10\;\;\;=\;\;\;6x^{2}-11x-10$

Report an Error

Example Question #4 : How To Use Foil In The Distributive Property

What are the factors of $x^{2}+11x+24$ ?

Possible Answers:

(x+11)(x+13)

(x+10)(x+1)

(x+8)(x+3)

(x+8)(x+4)

(x+6)(x+4)

Correct answer:

(x+8)(x+3)

Explanation:

To find the factors, you must determine which of the sets of factors result in the polynomial when multiplied together. Using the FOIL method, a set of factors with the form (x+a)(x+b) will result in $x^{2}+ax+bx+ab$ . Applying this format to the given equation of $x^{2}+11x+24$ , a+b must equal 11 and must equal 24. The only set that works is (x+8)(x+3) .

Report an Error

Example Question #5 : How To Use Foil In The Distributive Property

Expand:

(x+3)(2x-5)

Possible Answers:

$2x^{2}-2x-15$

$2x^{2}-x+15$

$2x^{2}+x-15$

$x^{2}-2x-15$

$x^{2}+2x-15$

Correct answer:

$2x^{2}+x-15$

Explanation:

If you use the FOIL method, you will multiply each expression individually. So, (x+3)(2x-5) becomes (x*2x)+(x*-5)+(3*2x)+(3*-5) , which simplifies to $2x^{2}+x-15$ .

Report an Error

Example Question #3 : How To Use Foil In The Distributive Property

Simplify the expression below.

$x^{2}y(2x + 3y)$

Possible Answers:

$5x^{2}y + 6x^{2}y^{2}$

$4x^{3}y + 5x^{2}y^{2}$

$2x^{2}y + 3xy^{2}$

$2x^{3}y + 3x^{2}y^{2}$

$3x^{2}y + 4xy^{2}$

Correct answer:

$2x^{3}y + 3x^{2}y^{2}$

Explanation:

$x^{2}y(2x + 3y)$

Use the distributive property to simplify the expression. In general, a(b+c) = ab + ac .

$x^{2}y(2x + 3y)=(x^{2}y*2x) + (x^{2}y*3y)$

Now we can begin to combine like terms through multiplication.

$(x^{2}y*2x) + (x^{2}y*3y)$

$(2x^{3}y)+(3x^2y^2)$

We cannot simplify further.

Report an Error

Example Question #6 : How To Use Foil In The Distributive Property

Multiply the binomials below.

(4x-7)(2x+6)

Possible Answers:

$8x^{2}-38x-42$

$8x^{2}+38x-42$

$8x^{2}-10x-42$

$8x^{2}+10x-42$

$8x^{2}-42$

Correct answer:

$8x^{2}+10x-42$

Explanation:

The FOIL method yields the products below.

First: $4x* 2x=8x^{2}$

Outside: 4x* 6=24x

Inside: -7* 2x=-14x

Last: -7* 6=-42

Add these four terms, and combine like terms, to obtain the product of the binomials.

$8x^{2}+24x+(-14x)+(-42)=8x^{2}+10x-42$

Report an Error

Example Question #7 : How To Use Foil In The Distributive Property

Factor the expression below.

x^3-3x^2-18x

Possible Answers:

x(x-6)(x-3)

x(x-6)(x+3)

x(x+6)(x-3)

(x^2-6x)(x^2+3x)

Correct answer:

x(x-6)(x+3)

Explanation:

x^3-3x^2-18x

First, factor out an , since it is present in all terms.

x(x^2-3x-18)

We need two factors that multiply to and add to .

-6*3=-18 and -6+3=-3

Our factors are and .

x(x-6)(x+3)

We can check our answer using FOIL to get back to the original expression.

First: (x)(x)=x^2

Outside: (x)(3)=3x

Inside: (x)(-6)=-6x

Last: (-6)(3)=18

Add together and combine like terms.

x^2+3x-6x-18=x^2-3x-18

Distribute the that was factored out first.

x(x^2-3x-18)=x^3-3x^2-18x

Report an Error

Example Question #8 : How To Use Foil In The Distributive Property

$\textup{What is the value of }\left ( 2p+4\right )\left ( p-5\right )\textup{?}$

Possible Answers:

$2p^{2}-20p-9$

$2p^{2}-6p-20$

$2p^{2}-14p-20$

$2p^{2}-p-20$

$2p^{2}+6p+20$

Correct answer:

$2p^{2}-6p-20$

Explanation:

$\textup{FOIL to distribute:} \left ( 2p+4\right )\left ( p-5\right )= 2p(p)+2p(-5)+4(p)+4(-5)$

$2p^{2}-10p+4p-20\;\;\;\;\;\;\;\;2p^{2}-6p-20$

Report an Error

Example Question #9 : How To Use Foil In The Distributive Property

Expand:

(x+4)(3x-2)

Possible Answers:

$3x^{2}+10x+8$

$3x^{2}+10x-8$

$3x^{2}+14x-8$

$x^{2}+14x+8$

$x^{2}+10x-8$

Correct answer:

$3x^{2}+10x-8$

Explanation:

To expand (x+4)(3x-2) , use the FOIL method, where you multiply each expression individually and take their sum. This will give you

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

or $3x^{2}+10x-8$

Report an Error

View Algebra Tutors

Shakeel
Certified Tutor

View Algebra Tutors

Raha
Certified Tutor

Amirkabir University of Technology, Bachelor of Science, Chemical Engineering. Wayne State University, Master of Science, Che...

View Algebra Tutors

Austyn
Certified Tutor

Morehead State University, Bachelor of Education, Mathematics Teacher Education. Morehead State University, Master of Arts, M...

All Algebra 1 Resources

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

Popular Subjects

Calculus Tutors in San Francisco-Bay Area, French Tutors in Denver, Computer Science Tutors in Dallas Fort Worth, Physics Tutors in San Francisco-Bay Area, SSAT Tutors in Boston, Algebra Tutors in Philadelphia, ISEE Tutors in Atlanta, French Tutors in Miami, ACT Tutors in Atlanta, English Tutors in Dallas Fort Worth

Popular Courses & Classes

ACT Courses & Classes in San Diego, ACT Courses & Classes in Atlanta, GRE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Phoenix, SSAT Courses & Classes in Boston, SAT Courses & Classes in Boston, GMAT Courses & Classes in Houston, ACT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Boston, GRE Courses & Classes in Atlanta

Popular Test Prep

SAT Test Prep in Denver, ACT Test Prep in San Diego, SAT Test Prep in New York City, ISEE Test Prep in Miami, SAT Test Prep in Washington DC, LSAT Test Prep in Phoenix, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Dallas Fort Worth, ISEE Test Prep in Denver, SSAT Test Prep in Phoenix

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 : Distributive Property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Use Foil In The Distributive Property

Example Question #2 : How To Use Foil In The Distributive Property

Example Question #3 : How To Use Foil In The Distributive Property

Example Question #4 : How To Use Foil In The Distributive Property

Example Question #5 : How To Use Foil In The Distributive Property

Example Question #3 : How To Use Foil In The Distributive Property

Example Question #6 : How To Use Foil In The Distributive Property

Example Question #7 : How To Use Foil In The Distributive Property

Example Question #8 : How To Use Foil In The Distributive Property

Example Question #9 : How To Use Foil In The Distributive Property

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: