Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to use FOIL in the distributive property

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Foil

$(\sqrt5+\sqrt3)^2=$

Possible Answers:

$8+\sqrt{15}$

$2+\sqrt{15}$

$8+2\sqrt{15 }$

$\sqrt{15}$

$2+2\sqrt{15}$

Correct answer:

$8+2\sqrt{15 }$

Explanation:

$(\sqrt5+\sqrt3)^2=(\sqrt5)^2+2\sqrt5\sqrt3+(\sqrt3)^2=5+2\sqrt{15}+3=8+2\sqrt{15}$

Report an Error

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

If (3x - 4)(3x + 4) = 2 , what is the value of 9x^2 ?

Possible Answers:

Correct answer:

Explanation:

Remember that (a – b )(a + b ) = a ²– b ².

We can therefore rewrite (3x – 4)(3x + 4) = 2 as (3x )²– (4)²= 2.

Simplify to find 9x²– 16 = 2.

Adding 16 to each side gives us 9x²= 18.

Report an Error

Example Question #3 : Foil

If g(x)=2x^2-2 and h(x)=x+4 , then which of the following is equivalent to g(h(x))-h(g(x)) ?

Possible Answers:

16x+28

2x^3+8x^2-2x-8

16x

-16x-28

Correct answer:

16x+28

Explanation:

We are asked to find the difference between g(h(x)) and h(g(x)), where g(x) = 2x² – 2 and h(x) = x + 4. Let's find expressions for both.

g(h(x)) = g(x + 4) = 2(x + 4)² – 2

g(h(x)) = 2(x + 4)(x + 4) – 2

In order to find (x+4)(x+4) we can use the FOIL method.

(x + 4)(x + 4) = x² + 4x + 4x + 16

g(h(x)) = 2(x² + 4x + 4x + 16) – 2

g(h(x)) = 2(x² + 8x + 16) – 2

Distribute and simplify.

g(h(x)) = 2x² + 16x + 32 – 2

g(h(x)) = 2x² + 16x + 30

Now, we need to find h(g(x)).

h(g(x)) = h(2x² – 2) = 2x² – 2 + 4

h(g(x)) = 2x² + 2

Finally, we can find g(h(x)) – h(g(x)).

g(h(x)) – h(g(x)) = 2x² + 16x + 30 – (2x² + 2)

= 2x² + 16x + 30 – 2x² – 2

= 16x + 28

The answer is 16x + 28.

Report an Error

Example Question #4 : Foil

The sum of two numbers is . The product of the same two numbers is . If the two numbers are each increased by one, the new product is . Find q-p in terms of .

Possible Answers:

2s+1

s+1

s^2

s+2

s-1

Correct answer:

s+1

Explanation:

Let the two numbers be x and y.

x + y = s

xy = p

(x + 1)(y + 1) = q

Expand the last equation:

xy + x + y + 1 = q

Note that both of the first two equations can be substituted into this new equation:

p + s + 1 = q

Solve this equation for q – p by subtracting p from both sides:

s + 1 = q – p

Report an Error

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

Expand the expression:

$\dpi{100} \small (x^{3}-4x)(6 + 12x^{2})$

Possible Answers:

$\dpi{100} \small 12x^{5}-42x^{3}-24x$

$\dpi{100} \small 22x^{2}$

$\dpi{100} \small 6x^{3} + 12x^{2}-24x-48$

$\dpi{100} \small 6x^{3} + 12x^{5}-24x-48x^{3}$

$\dpi{100} \small 42x^{3}+12x^{5}-24x$

Correct answer:

$\dpi{100} \small 12x^{5}-42x^{3}-24x$

Explanation:

When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.

$\dpi{100} \small (x^{3}-4x)(6 + 12x^{2})$

$\dpi{100} \small 6x^{3}+12x^{5}-24x-48x^{3}$

$\dpi{100} \small -42x^{3}+12x^{5}-24x$

$\dpi{100} \small 12x^{5}-42x^{3}-24x$

Report an Error

Example Question #6 : Foil

Expand the following expression:

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

Possible Answers:

$x^3+2x^2-8x-4$

$4x^3-4$

$4x^3+2x^2+8x+4$

$4x^3+4x-4$

$4x^3+2x^2-8x-4$

Correct answer:

$4x^3+2x^2-8x-4$

Explanation:

$(4x+2)(x^2-2)=(4x\times x^2)+(4x\times -2)+(2\times x^2) +(2\times -2)$

Which becomes

$4x^3-8x+2x^2-4$

Or, written better

$4x^3+2x^2-8x-4$

Report an Error

Example Question #7 : Foil

Which of the following is equal to the expression (3x - 1)(2x + 4) ?

Possible Answers:

{5x+3}

6x^2+10x-4

6x^2+2x+10

6x^2-4

6x^2-10

Correct answer:

6x^2+10x-4

Explanation:

Multiply using FOIL:

First = 3x(2x) = 6x²

Outter = 3x(4) = 12x

Inner = -1(2x) = -2x

Last = -1(4) = -4

Combine and simplify:

6x² + 12x - 2x - 4 = 6x² +10x - 4

Report an Error

Example Question #8 : Foil

Simplify the expression.

(2x^2-3x)(2y+a)

Possible Answers:

2x^2y - 2ax^2 - 3xy - 3ax

None of the other answers

-6x^3 + 2ay

4x^2y + 2ax^2 - 6xy - 3ax

-2axy

Correct answer:

4x^2y + 2ax^2 - 6xy - 3ax

Explanation:

Solve by applying FOIL:

First: 2x² * 2y = 4x²y

Outer: 2x² * a = 2ax²

Inner: –3x * 2y = –6xy

Last: –3x * a = –3ax

Add them together: 4x²y + 2ax² – 6xy – 3ax

There are no common terms, so we are done.

Report an Error

Example Question #9 : Foil

(6x - 2) (3x + 5) = ax^2 + dx + k

Given the equation above, what is the value of a-d+k ?

Possible Answers:

Correct answer:

Explanation:

(6x - 2) (3x + 5) = ax^2 + dx + k

Use FOIL to expand the left side of the equation.

(6x-2)(3x+5)=18x^2+30x-6x-10=18x^2+24x-10

18x^2+24x-10=ax^2+dx+k

From this equation, we can solve for , , and .

$18x^2=ax^2\rightarrow a=18$

$24x=dx\rightarrow d=24$

-10=k

Plug these values into a-d+k to solve.

a-d+k=(18)-(24)+(-10)=-16

Report an Error

Example Question #10 : Foil

Expand and simplify the expression.

4(x-5)(2x+10)

Possible Answers:

$8x^{2}-200$

8x^2-10x+10

$8x^{2}-200x$

$8x^{2}-80x-200$

$8x^{2}-40x+200$

Correct answer:

$8x^{2}-200$

Explanation:

4(x-5)(2x+10)

We can solve by FOIL, then distribute the $\small 4$ . Since all terms are being multiplied, you will get the same answer if you distribute the $\small 4$ before using FOIL.

First: x*2x=2x^2

Inside: -5*2x=-10x

Outside: x*10=10x

Last: -5*10=-50

Sum all of the terms and simplify. Do not forget the $\small 4$ in front of the quadratic!

4(2x^2-10x+10x-50)

4(2x^2-50)

Finally, distribute the $\small 4$ .

8x^2-200

Report an Error

View SAT Mathematics Tutors

Miriam
Certified Tutor

Washington University in St Louis, Bachelor in Arts, Biology, General.

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Irina
Certified Tutor

New York University, Bachelors, Biochemistry.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

SSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Atlanta, ISEE Courses & Classes in Miami, LSAT Courses & Classes in Houston, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Philadelphia, SSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Seattle, ACT Courses & Classes in Seattle, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ACT Test Prep in Washington DC, GRE Test Prep in Miami, GRE Test Prep in Phoenix, SSAT Test Prep in Chicago, ACT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Los Angeles, MCAT Test Prep in Houston, MCAT Test Prep in Chicago, ISEE Test Prep in Philadelphia, SAT Test Prep in Denver

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

SAT Math : How to use FOIL in the distributive property

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Foil

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

Example Question #3 : Foil

Example Question #4 : Foil

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

Example Question #6 : Foil

Example Question #7 : Foil

Example Question #8 : Foil

Example Question #9 : Foil

Example Question #10 : Foil

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: