Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Understanding Quadratic Equations

Solve: $(\sqrt{3}-\sqrt{2})(\sqrt2-\sqrt3)$

Possible Answers:

$2\sqrt6-5$

$2\sqrt3-5$

$\sqrt6-1$

$\sqrt6-5$

Correct answer:

$2\sqrt6-5$

Explanation:

Use the FOIL method to solve this problem.

(a+b)(c+d) = ac+ad+bc+bd

$(\sqrt3)(\sqrt2)+(\sqrt3)(-\sqrt3)+(-\sqrt2)(\sqrt2)+(-\sqrt2)(-\sqrt3)$

Multiply the terms together.

$\sqrt6-3-2+\sqrt6$

Combine like-terms.

The answer is: $2\sqrt6-5$

Report an Error

Example Question #61 : Quadratic Equations And Inequalities

Simplify: $(\sqrt{8}-3)(\sqrt8+6)$

Possible Answers:

$6\sqrt2-10$

$3\sqrt2-6$

$4\sqrt2-8$

$4\sqrt2-6$

$2\sqrt2+12$

Correct answer:

$6\sqrt2-10$

Explanation:

Solve the binomials by using the FOIL method. Following the template given:

(a+b)(c+d) = ac+ad+bc+bd

$(\sqrt8)(\sqrt8)+(\sqrt8)(6)+(-3)(\sqrt8)+(-3)(6)$

Simplify the expression.

$8+6\sqrt8-3\sqrt8-18$

Combine like-terms.

$3\sqrt8 -10$

We can rewrite $\sqrt8$ using common factors.

$\sqrt8 =\sqrt 4\cdot \sqrt2 = 2\sqrt2$

$3(2\sqrt2) -10 = 6\sqrt2-10$

The answer is: $6\sqrt2-10$

Report an Error

Example Question #63 : Quadratic Equations And Inequalities

Solve: (9-3x)(-2-8x)

Possible Answers:

24x^2+78x-18

24x^2-66x-18

24x^2-78x-18

$\textup{The answer is not given.}$

24x^2+66x-18

Correct answer:

24x^2-66x-18

Explanation:

Solve this expression using the FOIL method.

Use the following template for the FOIL method:

(a+b)(c+d) = ac+ad+bc+bd

Rewrite (9-3x)(-2-8x) .

(9)(-2)+(9)(-8x)+(-3x)(-2)+(-3x)(-8x)

Simplify the terms.

-18-72x+6x+24x^2

Combine like-terms and reorder the expression from highest to lowest power.

The answer is: 24x^2-66x-18

Report an Error

Example Question #64 : Quadratic Equations And Inequalities

Solve: (e^2+3)(e-1)

Possible Answers:

-e^3-3

e^3-e^2+3e-3

e^3-2e^2-3

e^3+e^2-3e-3

e^3+4e^2-3e-3

Correct answer:

e^3-e^2+3e-3

Explanation:

Simplify by using the FOIL method. Follow the template below to solve the problem.

(a+b)(c+d) = ac+ad+bc+bd

(e^2+3)(e-1) = (e^2)(e)+ (e^2)(-1)+(3)(e)+(3)(-1)

Simplify the terms.

e^3-e^2+3e-3

Do not combine unlike terms.

The answer is: e^3-e^2+3e-3

Report an Error

Example Question #221 : Intermediate Single Variable Algebra

Expand: $(5-\sqrt8)(4-\sqrt2)$

Possible Answers:

$24-13\sqrt2$

$\textup{The answer is not given.}$

$8-5\sqrt2$

$16-13\sqrt2$

Correct answer:

$24-13\sqrt2$

Explanation:

Use the FOIL method to solve this expression.

(a+b)(c+d) = ac+ad+bc+bd

Write out the terms.

$(5-\sqrt8)(4-\sqrt2)$

$=(5)(4)+(5)(-\sqrt2)+(-\sqrt8)(4)+(-\sqrt8)(-\sqrt2)$

Simplify the terms.

$=20-5\sqrt2-4\sqrt8+\sqrt{16}$

Rewrite the radicals that are not simplified.

$\sqrt8 = \sqrt{4\times 2} = \sqrt4 \times \sqrt2 = 2\sqrt2$

$\sqrt{16}=4$

Replace the terms.

$=20-5\sqrt2-4(2\sqrt2)+4$

$= 20-5\sqrt2-8\sqrt2+4 = 24-13\sqrt2$

The answer is: $24-13\sqrt2$

Report an Error

Example Question #66 : Quadratic Equations And Inequalities

Solve: (9x-8)(10x-7)

Possible Answers:

90x^2+17x+56

90x^2-17x+56

90x^2-143x-56

90x^2+143x-56

90x^2-143x+56

Correct answer:

90x^2-143x+56

Explanation:

Solve this by using the FOIL method.

(a+b)(c+d) = ac+ad+bc+bd

Substitute the given terms by the given formula.

(9x-8)(10x-7)

= (9x)(10x)+ (9x)(-7)+(-8)(10x)+(-8)(-7)

Simplify the terms.

90x^2-63x-80x+56

Combine like-terms.

The answer is: 90x^2-143x+56

Report an Error

Example Question #67 : Quadratic Equations And Inequalities

Solve: (-6+2x)(-9+3x)

Possible Answers:

6x^2-29x+54

6x^2-36x+54

-6x^2-36x+54

6x^2+54

6x^2-20x+54

Correct answer:

6x^2-36x+54

Explanation:

Use the FOIL method to expand the binomials.

(-6)(-9)+(-6)(3x)+(2x)(-9)+(2x)(3x)

Simplify the terms.

54-18x-18x+6x^2

Combine like terms.

The answer is: 6x^2-36x+54

Report an Error

Example Question #1362 : Algebra Ii

Solve: (-2x+5)(3x-9)

Possible Answers:

-6x^2+3x-45

6x^2-20x-45

-6x^2-2x-45

-6x^2+33x-45

-6x^2-33x+45

Correct answer:

-6x^2+33x-45

Explanation:

Solve this expression by using the FOIL method.

(-2x)(3x)+(-2x)(-9)+(5)(3x)+(5)(-9)

Simplify each term by order of operations.

-6x^2+18x+15x-45

Combine like-terms.

The answer is: -6x^2+33x-45

Report an Error

Example Question #1363 : Algebra Ii

Solve: $(\frac{1}{\sqrt2}-\sqrt2)(\frac{2}{\sqrt2}-\sqrt2)$

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to expand the terms. Follow the template for using this method.

(w+x)(y+z) = wy+wz+xy+xz

$(\frac{1}{\sqrt2}-\sqrt2)(\frac{2}{\sqrt2}-\sqrt2)$

$(\frac{1}{\sqrt2})(\frac{2}{\sqrt2})+(\frac{1}{\sqrt2})(-\sqrt2)+(-\sqrt2)(\frac{2}{\sqrt2})+(-\sqrt2)(-\sqrt2)$

Simplify all the terms.

1-1-2+2 = 0

The answer is:

Report an Error

Example Question #62 : Quadratic Equations And Inequalities

Solve: (7x-4)(3-9x)

Possible Answers:

-63x^2-57x-12

-63x^2-24x-12

-63x^2-15x-12

-63x^2+57x-12

-63x^2-15x-12

Correct answer:

-63x^2+57x-12

Explanation:

Use the FOIL method to simplify the expression. Multiply each term of the first binomial with the terms of the second binomial.

(7x)(3)+(7x)(-9x)+(-4)(3)+(-4)(-9x)

Simplify the expression.

21x-63x^2-12+36x

Combine like-terms and reorder all the terms from highest to lowest order.

The answer is: -63x^2+57x-12

Report an Error

View Algebra 2 Tutors

Lilian Natalia
Certified Tutor

University of Texas Rio Grande Valley, Bachelor of Science, Mechanical Engineering. University of Texas Rio Grande Valley, Ma...

View Algebra 2 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Algebra 2 Tutors

Nicholas
Certified Tutor

Salem State University, Bachelor of Science, GIS Technology.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Seattle, Chemistry Tutors in Chicago, Computer Science Tutors in Seattle, Math Tutors in Houston, French Tutors in Chicago, MCAT Tutors in Denver, SSAT Tutors in Denver, Reading Tutors in San Francisco-Bay Area, ISEE Tutors in Miami, ISEE Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Chicago, GMAT Courses & Classes in San Diego, ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in Denver, ISEE Courses & Classes in Washington DC, Spanish Courses & Classes in Houston, SSAT Courses & Classes in Houston, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in Washington DC, GMAT Test Prep in Boston, ACT Test Prep in Washington DC, MCAT Test Prep in Washington DC, LSAT Test Prep in Houston, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Miami, SSAT Test Prep in Los Angeles, GMAT Test Prep in Philadelphia, ACT Test Prep in San Diego

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 II : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Understanding Quadratic Equations

Example Question #61 : Quadratic Equations And Inequalities

Example Question #63 : Quadratic Equations And Inequalities

Example Question #64 : Quadratic Equations And Inequalities

Example Question #221 : Intermediate Single Variable Algebra

Example Question #66 : Quadratic Equations And Inequalities

Example Question #67 : Quadratic Equations And Inequalities

Example Question #1362 : Algebra Ii

Example Question #1363 : Algebra Ii

Example Question #62 : Quadratic Equations And Inequalities

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: