Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to subtract exponential variables

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Subtract Exponential Variables

Simplify the expression:

$7x^{3} - 5x^{2} + 9x^{3}$

Possible Answers:

$16 x^{3} - 5x^{2}$

$2x^{2} + 9x^{3}$

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

The expression cannot be simplified further.

$11x^{5}$

Correct answer:

$16 x^{3} - 5x^{2}$

Explanation:

Group, then collect like terms:

$7x^{3} - 5x^{2} + 9x^{3}$

$=7x^{3} + 9x^{3} - 5x^{2}$

$=\left ( 7 + 9 \right )x^{3} - 5x^{2}$

$=16x^{3} - 5x^{2}$

Report an Error

Example Question #2 : How To Subtract Exponential Variables

Simplify:

$\frac{(x+2y)^{2} - (x - 2y)^{2}}{xy}$

Possible Answers:

-8xy

8xy

$\frac{2x^{2}+8y^{2}}{xy}$

Correct answer:

Explanation:

$\frac{(x+2y)^{2} - (x - 2y)^{2}}{xy}$

$=\frac{(x^{2}+4xy+4y^{2})-(x^{2}-4xy+4y^{2})}{xy}$

$=\frac{x^{2}-x^{2}+4xy+4xy+4y^{2}-4y^{2}}{xy}$

$=\frac{8xy}{xy} = 8$

Report an Error

Example Question #3 : How To Subtract Exponential Variables

Assume that $x \neq 0$ . Which of the following expressions is equivalent to:

$\frac{\left (x+1 \right ) ^{3} - \left ( x^{3 } + 1\right ) }{x^{2}}$ ?

Possible Answers:

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

$3 + \frac{ 3 }{x}$

$\frac{ 2 }{x} + \frac{ 2 }{x^{2}}$

$2 + \frac{ 2 }{x}$

Correct answer:

$3 + \frac{ 3 }{x}$

Explanation:

$\frac{\left (x+1 \right ) ^{3} - \left ( x^{3 } + 1\right ) }{x^{2}}$

$= \frac{\left (x^{3} +3x^{2} + 3x + 1 ) - \left ( x^{3 } + 1\right ) }{x^{2}}$

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

$= \frac{3x^{2} + 3x }{x^{2}}$

$= \frac{3x^{2} }{x^{2}} + \frac{ 3x }{x^{2}}$

$=3 + \frac{ 3 }{x}$

Report an Error

Example Question #1 : How To Subtract Exponential Variables

If $x\neq 0$ , simplify:

$\frac{(x-1)^2-(x^2-1)}{x-1}$

Possible Answers:

x-1

-2(x-1)

2(x-1)

Correct answer:

Explanation:

$\frac{(x-1)^2-(x^2-1)}{x-1}=\frac{(x^2-2x+1)-(x^2-1)}{x-1}$

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

$=\frac{2(1-x)}{x-1}$

$=\frac{2(1-x)}{-1(1-x)}$

$=\frac{2}{-1}=-2$

Report an Error

Example Question #1 : How To Subtract Exponential Variables

If $x,y\neq 0$ , simplify:

$\frac{(x+y)^2-(x-y)^2}{2xy}$

Possible Answers:

4xy

Correct answer:

Explanation:

$\frac{(x+y)^2-(x-y)^2}{2xy}=\frac{(x^2+2xy+y^2)-(x^2-2xy+y^2)}{2xy}$

$=\frac{x^{2}-x^{2}+y^{2}-y^{2}+2xy+2xy}{2xy}$

$=\frac{4xy}{xy}=4$

Report an Error

Example Question #1 : How To Subtract Exponential Variables

If $x\neq 0$ , simplify:

$\frac{(x^{2}+3)^2-(x^2-3)^2}{6x^2}$

Possible Answers:

2xy

$\frac{2}{x}$

Correct answer:

Explanation:

$\frac{(x^{2}+3)^2-(x^2-3)^2}{6x^2}=\frac{(x^4+6x^2+9)-(x^4-6x^2+9)}{6x^2}$

$=\frac{x^4-x^4+6x^2+6x^2+9-9}{6x^2}$

$=\frac{12x^2}{6x^2}=2$

Report an Error

Example Question #7 : How To Subtract Exponential Variables

If $x,y\neq 0$ , simplify:

$\frac{(x^2+y^2)-(x-y)^{2}}{xy}$

Possible Answers:

2xy

Correct answer:

Explanation:

$\frac{(x^2+y^2)-(x-y)^{2}}{xy}=\frac{x^2+y^2-(x^2-2xy+y^2)}{xy}$

$=\frac{x^2-x^2+y^2-y^2+2xy}{xy}$

$=\frac{2xy}{xy}=2$

Report an Error

Example Question #1 : How To Subtract Exponential Variables

If $x\neq 0$ , simplify:

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

Possible Answers:

$\frac{4}{x}$

$\frac{16}{x}$

Correct answer:

Explanation:

$(x+\frac{4}{x})^2-(x-\frac{4}{x})^2=(x^{2}+2\times x\times \frac{4}{x}+\frac{16}{x^2})-(x^{2}-2\times x\times \frac{4}{x}+\frac{16}{x^2})$

$=(x^{2}+8+\frac{16}{x^2})-(x^{2}-8+\frac{16}{x^2})$

$=x^2-x^2+8+8+\frac{16}{x^2}-\frac{16}{x^2}$

=8+8=16

Report an Error

Example Question #1 : How To Subtract Exponential Variables

Simplify the following expression:

12x^6-9x^6

Possible Answers:

2x^6

3x^6

21x^6

Correct answer:

3x^6

Explanation:

Simplify the following expression:

12x^6-9x^6

We can treat this basically as a regular subtraction problem.

We want to subtract our coefficients, while leaving the exponents the same.

12x^6-9x^6=3x^6

Report an Error

View Tutors

Jennifer
Certified Tutor

McKendree University, Bachelor in Business Administration, Accounting and Business Management. Lindenwood University, Masters...

View Tutors

Myung Hee
Certified Tutor

Pukyung National University, Bachelor of Science, Japanese Studies. University of Padova, Master of Science, International Bu...

View Tutors

Gregory
Certified Tutor

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

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Atlanta, Chemistry Tutors in Atlanta, French Tutors in Chicago, MCAT Tutors in Atlanta, English Tutors in New York City, Biology Tutors in Phoenix, ACT Tutors in Phoenix, Statistics Tutors in Atlanta, English Tutors in Dallas Fort Worth, SSAT Tutors in Phoenix

Popular Courses & Classes

Spanish Courses & Classes in Phoenix, Spanish Courses & Classes in Chicago, GRE Courses & Classes in Boston, LSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Seattle, ISEE Courses & Classes in Seattle, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Houston, MCAT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in New York City, SAT Test Prep in San Diego, GMAT Test Prep in Denver, ACT Test Prep in Denver, LSAT Test Prep in New York City, SSAT Test Prep in Miami, LSAT Test Prep in Miami, MCAT Test Prep in Miami, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Philadelphia

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

ISEE Upper Level Math : How to subtract exponential variables

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Subtract Exponential Variables

Example Question #2 : How To Subtract Exponential Variables

Example Question #3 : How To Subtract Exponential Variables

Example Question #1 : How To Subtract Exponential Variables

Example Question #1 : How To Subtract Exponential Variables

Example Question #1 : How To Subtract Exponential Variables

Example Question #7 : How To Subtract Exponential Variables

Example Question #1 : How To Subtract Exponential Variables

Example Question #1 : How To Subtract Exponential Variables

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: