We are open Saturday and Sunday!

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

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 … 15 16 Next →

Example Question #71 : Quadratic Equations And Inequalities

Solve: $(\pi-3)(1-3\pi)$

Possible Answers:

$-3\pi^2-8\pi-3$

$-3\pi^2+10\pi-3$

$4\pi^2-10$

$-3\pi^2-10\pi-3$

$-3\pi^2+8\pi-3$

Correct answer:

$-3\pi^2+10\pi-3$

Explanation:

We can expand this expression by using the FOIL method.

Follow the given template and substitute.

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

$(\pi-3)(1-3\pi)$

$=(\pi)(1)+(\pi)(-3\pi)+(-3)(1)+(-3)(-3\pi)$

Simplify the terms.

$=\pi-3\pi^2-3+9\pi$

Combine like-terms.

The answer is: $-3\pi^2+10\pi-3$

Report an Error

Example Question #51 : Foil

Solve the expression: (4-x)(7+6x)

Possible Answers:

-6x^2+17x+28

-6x^2-17x+28

-6x^2+31x+28

-6x^2-12x+38

-6x^2-31x+28

Correct answer:

-6x^2+17x+28

Explanation:

Use the FOIL method to simplify this expression.

Multiply each term of the first binomial with the terms of the second binomial.

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

Simplify the expression.

28+24x-7x-6x^2

Combine like terms.

The answer is: -6x^2+17x+28

Report an Error

Example Question #73 : Quadratic Equations And Inequalities

Evaluate: $(\sqrt{3}-3)(\sqrt5-5)$

Possible Answers:

$\sqrt{15}-8\sqrt5 +15$

$-7\sqrt{15} +15$

$-7\sqrt5 +15$

$\sqrt{15}-8\sqrt3 +15$

$\sqrt{15}-5\sqrt3 -3\sqrt5 +15$

Correct answer:

$\sqrt{15}-5\sqrt3 -3\sqrt5 +15$

Explanation:

Use the FOIL method to simplify this expression. Use the following template:

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

$(\sqrt{3}-3)(\sqrt5-5)$

$= (\sqrt{3})(\sqrt{5 })+(\sqrt{3})(-5)+(-3)(\sqrt{5})+(-3)(-5)$

Simplify each term. Uncommon radical terms cannot be combined.

The answer is: $\sqrt{15}-5\sqrt3 -3\sqrt5 +15$

Report an Error

Example Question #74 : Quadratic Equations And Inequalities

Evaluate: (x^2+3)(-9x^2+4)

Possible Answers:

-9x^4-16x^2+12

-9x^4-23x^2+12

-9x^4+23x^2+12

-9x^4-48x^2+12

-9x^4-31x^2+12

Correct answer:

-9x^4-23x^2+12

Explanation:

Use the FOIL method to simplify this expression. Use the following formula as a template to solve the expression:

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

For (x^2+3)(-9x^2+4) ,

(x^2)(-9x^2)+(x^2)(4)+(3)(-9x^2)+(3)(4)

Simplify all the terms.

-9x^4+4x^2-27x^2+12

Combine like terms.

The answer is: -9x^4-23x^2+12

Report an Error

Example Question #75 : Quadratic Equations And Inequalities

Simplify the binomials: $(\frac{2}{3}x+3)(\frac{2}{5}x+2)$

Possible Answers:

$\frac{1}{2}x^2+\frac{14}{5}x+6$

$\frac{4}{15}x^2+\frac{38}{15}x+6$

$\frac{1}{2}x^2+\frac{38}{15}x+6$

$\frac{4}{15}x^2+\frac{14}{5}x+6$

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

Correct answer:

$\frac{4}{15}x^2+\frac{38}{15}x+6$

Explanation:

Use the FOIL method to simplify this expression.

$(\frac{2}{3}x+3)(\frac{2}{5}x+2)$

$=(\frac{2}{3}x)(\frac{2}{5}x)+(\frac{2}{3}x)(2)+(3)(\frac{2}{5}x)+(3)(2)$

Simplify all the terms in parentheses.

$\frac{4}{15}x^2+\frac{4}{3}x+\frac{6}{5}x+6$

Combine the center two terms.

$\frac{4}{3}x+\frac{6}{5}x = \frac{20}{15}x+\frac{18}{15}x = \frac{38}{15}x$

The answer is: $\frac{4}{15}x^2+\frac{38}{15}x+6$

Report an Error

Example Question #76 : Quadratic Equations And Inequalities

Evaluate: (4x-6)(7x+3)

Possible Answers:

28x^2-54x-18

28x^2-30x-18

28x^2-46x-18

28x^2+54x-18

28x^2+30x-18

Correct answer:

28x^2-30x-18

Explanation:

Use the FOIL method to simplify this expression.

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

Follow this equation for the given problem.

(4x-6)(7x+3) = (4x)(7x)+(4x)(3)+(-6)(7x)+(-6)(3)

Simplify the parentheses.

28x^2+12x-42x-18

Combine like-terms.

The answer is: 28x^2-30x-18

Report an Error

Example Question #77 : Quadratic Equations And Inequalities

Solve: (5x+18)(3x-1)

Possible Answers:

15x^2-3x-18

15x^2+59x-18

15x^2+49x-18

15x^2-59x-18

15x^2-49x-18

Correct answer:

15x^2+49x-18

Explanation:

Solve the expression by using the FOIL method. Follow the template below.

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

(5x)(3x)+(5x)(-1)+(18)(3x)+(18)(-1)

Simplify the terms.

15x^2-5x+54x-18

Combine like-terms.

15x^2-5x+54x-18 = 15x^2+49x-18

The answer is: 15x^2+49x-18

Report an Error

Example Question #78 : Quadratic Equations And Inequalities

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

Possible Answers:

-6x^2-33x-27

-6x^2+21x-27

6x^2-33x-27

-6x^2-21x-27

-6x^2+33x-27

Correct answer:

-6x^2+33x-27

Explanation:

Simplify the terms by using the FOIL method.

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

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

Simplify the terms in parentheses.

27x-6x^2-27+6x

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

The answer is: -6x^2+33x-27

Report an Error

Example Question #79 : Quadratic Equations And Inequalities

Evaluate: $(\sqrt{3}+\sqrt{8})(\sqrt{3}-\sqrt2)$

Possible Answers:

$\sqrt{6}-1$

$7-2\sqrt6$

$3\sqrt{2}-7$

$2\sqrt{3}-1$

$\sqrt{6}-1$

Correct answer:

$\sqrt{6}-1$

Explanation:

Evaluate this by using the FOIL method.

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

Use this equation to determine the value of the problem.

$(\sqrt{3}+\sqrt{8})(\sqrt{3}-\sqrt2)$

$(\sqrt3)(\sqrt3)+(\sqrt3)(-\sqrt2)+(\sqrt8)(\sqrt3)+(\sqrt8)(-\sqrt2)$

Simplify the expression.

$3-\sqrt6+\sqrt{24}-\sqrt{16}$

Simplify all radicals, if possible.

$3-\sqrt6+2\sqrt{6}-4 = \sqrt{6}-1$

The answer is: $\sqrt{6}-1$

Report an Error

Example Question #80 : Quadratic Equations And Inequalities

Solve: $(\frac{1}{2}x-3)(\frac{2}{3}x+4)$

Possible Answers:

$\frac{1}{3}x^2-2x+12$

$\frac{1}{3}x^2+12$

$\frac{1}{3}x^2-4x+12$

$\frac{1}{3}x^2-12$

$\frac{1}{3}x^2-x+12$

Correct answer:

$\frac{1}{3}x^2-12$

Explanation:

Solve by using the FOIL method.

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

Simplify the expression given.

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

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

Simplify the terms. To multiply a fraction with another number, multiply the numerator with the whole number.

$\frac{1}{3}x^2+2x-2x-12 = \frac{1}{3}x^2-12$

The answer is: $\frac{1}{3}x^2-12$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 … 15 16 Next →

View Algebra 2 Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Algebra 2 Tutors

Humaira
Certified Tutor

North South University, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

All Algebra II Resources

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

Popular Subjects

GRE Tutors in New York City, Reading Tutors in Dallas Fort Worth, ACT Tutors in Atlanta, Biology Tutors in Atlanta, Biology Tutors in San Francisco-Bay Area, Statistics Tutors in Seattle, GMAT Tutors in Seattle, English Tutors in Dallas Fort Worth, Biology Tutors in Boston, Spanish Tutors in Boston

Popular Courses & Classes

MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Phoenix, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in Miami, LSAT Courses & Classes in Miami, ISEE Courses & Classes in Seattle, ISEE Courses & Classes in Los Angeles, ISEE Courses & Classes in Atlanta, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Houston, SSAT Test Prep in Atlanta, ACT Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Diego, MCAT Test Prep in Phoenix, ISEE Test Prep in Seattle, SAT Test Prep in Atlanta, SSAT Test Prep in Denver, SSAT Test Prep in Dallas Fort Worth, 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 II : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Quadratic Equations And Inequalities

Example Question #51 : Foil

Example Question #73 : Quadratic Equations And Inequalities

Example Question #74 : Quadratic Equations And Inequalities

Example Question #75 : Quadratic Equations And Inequalities

Example Question #76 : Quadratic Equations And Inequalities

Example Question #77 : Quadratic Equations And Inequalities

Example Question #78 : Quadratic Equations And Inequalities

Example Question #79 : Quadratic Equations And Inequalities

Example Question #80 : 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: