Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Simplifying Expressions

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 #1993 : Algebra Ii

Simplify the expression: 6ab(a^2-b)-ab

Possible Answers:

6ab^3-6ab^2-ab

12a^3b-ab

6a^3b-7ab^2

-13a^3b^3

6a^3b-6ab^2-ab

Correct answer:

6a^3b-6ab^2-ab

Explanation:

Distribute the first term with the binomial.

6ab(a^2-b) = 6ab(a^2)-6ab(b)= 6a^3b-6ab^2

Subtract the last term with this expression. Do not combine the terms as one unit. There are no like-terms, and the terms cannot simplified any further.

The answer is: 6a^3b-6ab^2-ab

Report an Error

Example Question #151 : Basic Single Variable Algebra

Simplify the expression: $6xy(-2x-2y+\frac{x}{6})$

Possible Answers:

-11x^2y+12xy^2

-11x^2y-12xy^2

-13x^2y-12xy^2

-12x^2y-12xy^2+y

-12x^2y-12xy^2

Correct answer:

-11x^2y-12xy^2

Explanation:

Multiply the first term with every term inside the parentheses.

6xy(-2x) = -12x^2y

6xy(-2y) = -12xy^2

$6xy(\frac{x}{6}) =x^2y$

Sum the terms.

-12x^2y-12xy^2+x^2y

Combine like-terms.

The answer is: -11x^2y-12xy^2

Report an Error

Example Question #61 : Simplifying Expressions

Simplify the following expression:

$512^\frac{5}{9}-(\frac{1}{16})^\frac{-3}{4}$

Possible Answers:

Correct answer:

Explanation:

First, focus on the first term $512^\frac{5}{9}$ . By the rules for multiplying exponents,

$512^\frac{5}{9}=(512^\frac{1}{9})^5$ .

Since 2^9=512 , $512^\frac{1}{9}=2$ . Hence,

$(512^\frac{1}{9})^5=2^5=32$ .

Now focus on the second term, $(\frac{1}{16})^\frac{-3}{4}$ . Since the exponent is negative, we must rewrite this expression as the reciprocal of the base to the positive $\frac{3}{4}$ power:

$(\frac{1}{16})^\frac{-3}{4}=16^\frac{3}{4}$

By the rules for multiplying exponents,

$16^\frac{3}{4}=(16^\frac{1}{4})^3$

Since 2^4=16 , $16^\frac{1}{4}=2$ . Hence,

$(16^\frac{1}{4})^3=2^3=8$ .

Substituting these simplified terms into the original expression yields

$512^\frac{5}{9}-(\frac{1}{16})^\frac{-3}{4}=32-8=24$ .

Hence, is the correct answer.

Report an Error

Example Question #1994 : Algebra Ii

Simplify: -4(2x+3)+2(8x-1)

Possible Answers:

14x-8

8x-2

8x-14

8x+14

4x-14

Correct answer:

8x-14

Explanation:

First, use the distributive property:

-8x-12+16x-2

Now simplify by combining your like terms:

-8x+16x=8x

-12-2=-14

Therefore, your final answer is:

8x-14

Report an Error

Example Question #61 : Simplifying Expressions

Simplify: $7ab^2(a^2-b^{-2})$

Possible Answers:

7a^3b^2-7a

$a^3b^2-\frac{a}{b^4}$

a^3b^2-a

7a^3b^2

$7a^3b^2-\frac{7a}{b^4}$

Correct answer:

7a^3b^2-7a

Explanation:

Distribute the outer term with both terms inside the parentheses.

$7ab^2(a^2-b^{-2}) = (7ab^2)(a^2)- (7ab^2)(b^{-2})$

When similar bases are multiplied, we can add the exponents of that base.

Simplify the terms.

$(7ab^2)(a^2)- (7ab^2)(b^{-2}) = 7a^3b^2- 7ab^0$

Any term besides zero raised to the power of zero equals one.

The answer is: 7a^3b^2-7a

Report an Error

Example Question #151 : Basic Single Variable Algebra

Given the expression $\frac{w}{x}-\frac{w}{y}-\frac{w}{z}$ , what must be the numerator of the simplified form?

Possible Answers:

wyz-wxz-wxy

xyz-wyz-wxz

yz+xz+xy

yz-xz-xy

Correct answer:

wyz-wxz-wxy

Explanation:

To determine the number, we will need to find the least common denominator by multiplying all three denominators together.

(x)(y)(z)=xyz

Simplify the fractions.

$\frac{w}{x}-\frac{w}{y}-\frac{w}{z} = \frac{wyz}{xyz}-\frac{wxz}{xyz}-\frac{wxy}{xyz}$

The answer is: wyz-wxz-wxy

Report an Error

Example Question #1995 : Algebra Ii

If a=-2 and b=-3 , what does (a+b)^2-(a-b)^2 equal?

Possible Answers:

Correct answer:

Explanation:

Substitute the terms into the expression.

(a+b)^2-(a-b)^2 = ((-2)+(-3))^2-((-2)-(-3))^2

Simplify the terms by order of operation. Start with the inner parentheses.

(-5)^2-(1)^2 = 25-1 = 24

The answer is:

Report an Error

Example Question #152 : Basic Single Variable Algebra

Simplify: abc^2(ac-bc^2)

Possible Answers:

2abc^2-4bc

2a^2bc^3-2ab^2c^4

2abc^2-bc

a^2bc^3-ab^2c^4

a^2bc^3-2ab^2c^2

Correct answer:

a^2bc^3-ab^2c^4

Explanation:

In order to simplified the expression, we will need to distribute the outer term through the terms inside the parentheses.

abc^2(ac-bc^2)=abc^2(ac)-abc^2(bc^2)

Distribute the terms.

The answer is: a^2bc^3-ab^2c^4

Report an Error

Example Question #153 : Basic Single Variable Algebra

Simplify: $\frac{\frac{y}{x(x+1)}}{1+\frac{y}{x(x+1)}}$

Possible Answers:

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

$\frac{y}{x+y}$

$\frac{x}{x+y}$

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

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

Correct answer:

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

Explanation:

Simplify the complex fraction by parts.

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

Replace the terms.

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

Simplify the denominator. Convert the integer using the least common denominator, which is x^2+x .

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

Replace this term in the denominator.

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

Rewrite this using a division sign.

$\frac{\frac{y}{x^2+x}}{ \frac{x^2+x+y}{x^2+x}} = \frac{y}{x^2+x} \div\frac{x^2+x+y}{x^2+x}$

Change the sign to multiplication and take the reciprocal of the second term.

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

Cancel the common terms.

The answer is: $\frac{y}{x^2+x+y}$

Report an Error

Example Question #2001 : Algebra Ii

Evaluate a^2+b^2 if 2a+2 =4 and b=5 .

Possible Answers:

Correct answer:

Explanation:

The value of will need to be solved for. Subtract two from both sides given the following equation.

2a+2 =4

2a+2 -2=4-2

2a=2

Divide by two on both sides.

$\frac{2a}{2}=\frac{2}{2}$

a=1

Now that we know the value of a and b, we substitute both values in the expression a^2+b^2 .

a^2+b^2 = 1^2+5^2 = 1+25= 26

The answer is:

Report an Error

View Algebra 2 Tutors

John
Certified Tutor

The University of Texas at Arlington, Bachelor of Science, Mathematics. Stanford University, Master of Science, Aerospace Eng...

View Algebra 2 Tutors

Michael
Certified Tutor

University of California-San Diego, Bachelors, Physics with specialization in Earth Science. University of California-San Die...

View Algebra 2 Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

All Algebra II Resources

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

Popular Subjects

Computer Science Tutors in San Francisco-Bay Area, Statistics Tutors in Chicago, LSAT Tutors in San Diego, Physics Tutors in Washington DC, Algebra Tutors in Atlanta, SAT Tutors in Washington DC, ISEE Tutors in Washington DC, ISEE Tutors in Houston, Math Tutors in Houston, ACT Tutors in Los Angeles

Popular Courses & Classes

SAT Courses & Classes in San Diego, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in San Diego, SAT Courses & Classes in New York City, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Washington DC, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Seattle, SSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Denver, ACT Test Prep in Phoenix, LSAT Test Prep in Washington DC, ACT Test Prep in Washington DC, SSAT Test Prep in Phoenix, SSAT Test Prep in San Diego, SSAT Test Prep in Miami, SSAT Test Prep in Houston, GMAT Test Prep in Phoenix, ACT Test Prep in Houston

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 : Simplifying Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1993 : Algebra Ii

Example Question #151 : Basic Single Variable Algebra

Example Question #61 : Simplifying Expressions

Example Question #1994 : Algebra Ii

Example Question #61 : Simplifying Expressions

Example Question #151 : Basic Single Variable Algebra

Example Question #1995 : Algebra Ii

Example Question #152 : Basic Single Variable Algebra

Example Question #153 : Basic Single Variable Algebra

Example Question #2001 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: