Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : 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 #3 : Monomials

Find the product:

$\small 7n(8n-2)$

Possible Answers:

$\small n^2+14$

$\small n-14$

$\small 56n^2-14n$

$\small n^2-14n$

Correct answer:

$\small 56n^2-14n$

Explanation:

First, mulitply the mononomial by the first term of the polynomial:

$\small 7n\times8n\ = 56n^2$

Second, multiply the monomial by the second term of the polynomial:

$\small 7n\times (-2)\ = -14n$

Add the terms together:

$\small 56n^2\ +\ (-14n)\ = 56n^2-14n$

Report an Error

Example Question #51 : Expressions

Multiply, expressing the product in simplest form:

$\small \frac{15x^{5}}{14y^{3}} \cdot \frac{21y^{2} }{25x^{3}}$

Possible Answers:

$\small \small \small \frac{9 x^{2}y}{10 }$

$\small \small \small \small \frac{10 x^{2}}{9y }$

$\small \small \frac{9 x^{2}}{10 y}$

$\small \small \small \small \small \frac{10 y}{9x^{2} }$

$\small \small \small \small \frac{9 y}{10x^{2} }$

Correct answer:

$\small \small \frac{9 x^{2}}{10 y}$

Explanation:

Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:

$\small \small \small \small \frac{15x^{5}}{14y^{3}} \cdot \frac{21y^{2} }{25x^{3}} = \small \small \small \small \frac{3x^{5}}{2y^{3}} \cdot \frac{3y^{2} }{5x^{3}} = \frac{3x^{5} \cdot 3y^{2}}{5x^{3} \cdot 2y^{3}} = \frac{3 \cdot 3 \cdot x^{5} y^{2}}{5\cdot 2\cdot x^{3} y^{3}} = \frac{9 x^{5} y^{2}}{10 x^{3} y^{3}}$

Now use the quotient rule on the variables by subtracting exponents:

$\small \frac{9 x^{5} y^{2}}{10 x^{3} y^{3}} = \frac{9 x^{5-3}}{10 y^{3-2}} = \frac{9 x^{2}}{10 y^{1}} = \frac{9 x^{2}}{10 y}$

Report an Error

Example Question #2 : Simplifying Expressions

Simplify the following:

$\frac{2xy^2}{3yz^2} \times \frac{15y^2z}{14x^2y}$

Possible Answers:

$\frac{5xy^2}{7z}$

$\frac{5y^2}{7xz}$

$\frac{7y^2}{5x^2z}$

$\frac{5xz}{7y^2}$

Correct answer:

$\frac{5y^2}{7xz}$

Explanation:

In this problem, you have two fractions being multiplied. You can first simplify the coefficients in the numerators and denominators. You can divide and cancel the 2 and 14 each by 2, and the 3 and 15 each by 3:

$\frac{2xy^2}{3yz^2} \times \frac{15y^2z}{14x^2y} = \frac{xy^2}{yz^2} \times \frac{5y^2z}{7x^2y}$

You can multiply the two numerators and two denominators, keeping in mind that when multiplying like variables with exponents, you simplify by adding the exponents together:

$\frac{xy^2}{yz^2} \times \frac{5y^2z}{7x^2y} = \frac{5xy^4z}{7x^2y^2z^2}$

Any variables that are both in the numerator and denominator can be simplified by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable to the denominator to keep the exponent positive:

$\frac{5xy^4z}{7x^2y^2z^2} = \frac{5y^2}{7xz}$

Report an Error

Example Question #2 : How To Factor A Variable

Factor the expression:

$\small \small 2xy^3-14xy^2+9xy$

Possible Answers:

$\small 2xy(y^2-7xy+9)$

$\small xy^3(2-14xy^2+9xy)$

$\small x(2y^3-14y^2+9y)$

$\small 2xy^3(-14xy^2+9xy)$

$\small xy(2y^2-14y+9)$

Correct answer:

$\small xy(2y^2-14y+9)$

Explanation:

To find the greatest common factor, we need to break each term into its prime factors:

$\small 2xy^3=2 \cdot x \cdot y \cdot y \cdot y$

$\small 14xy^2 = 2 \cdot 7 \cdot x \cdot y \cdot y$

$\small 9xy = 3 \cdot 3 \cdot x \cdot y$

Looking at which terms all three expressions have in common; thus, the GCF is $\small xy$ . We then factor this out: $\small \small xy(2y^2 -14y +9)$ .

Report an Error

Example Question #52 : Expressions

Expand: 8x(3x+7)

Possible Answers:

24x^2 + 56

24x^2 + 56x

11x^2 + 15x

24x + 56

11x + 15

Correct answer:

24x^2 + 56x

Explanation:

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

Report an Error

Example Question #53 : Expressions

Simplify:

-5(x+15)-3x

Possible Answers:

2x-75

2x+15

None of the other answers are correct.

-8x-75

-8x+15

Correct answer:

-8x-75

Explanation:

First, distribute –5 through the parentheses by multiplying both terms by –5.

-5(x+15)-3x=-5x-75-3x

Then, combine the like-termed variables (–5x and –3x).

-5x-75-3x=-8x-75

Report an Error

Example Question #54 : Expressions

Expand:

$\frac{1}{3}(2x^2-6)(4x-\frac{2}{3})$

Possible Answers:

$2\frac{2}{3}x^3-\frac{4}{9}x^2+8x+1\frac{1}{3}$

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x-1\frac{1}{3}$

$-2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

$2\frac{2}{3}x^3+\frac{4}{9}x^2-8x+1\frac{1}{3}$

Correct answer:

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

Explanation:

First, FOIL:

$\frac{1}{3}(8x^3-\frac{4}{3}x^2-24x+\frac{12}{3})$

Simplify:

$\frac{1}{3}(8x^3-\frac{4}{3}x^2-24x+4)$

Distribute the $\frac{1}{3}$ through the parentheses:

$\frac{8}{3}x^3-\frac{4}{9}x^2-\frac{24}{3}x+\frac{4}{3}$

Rewrite to make the expression look like one of the answer choices:

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

Report an Error

Example Question #83 : Polynomial Operations

Simplify the expression.

$15x^{3}y^{2}+8x^{2}+3x^{3}y^{2}-4x^{2}$

Possible Answers:

None of the other answers are correct.

$18x^{3}y^{2}+4x^{2}$

$18x^{3}y^{2}-4x^{2}$

$22x^3y^{2}x^{2}$

$22x^{6}y^{4}$

Correct answer:

$18x^{3}y^{2}+4x^{2}$

Explanation:

When simplifying polynomials, only combine the variables with like terms.

$15x^{3}y^{2}$ can be added to $3x^{3}y^{2}$ , giving $18x^{3}y^{2}$ .

$4x^{2}$ can be subtracted from $8x^{2}$ to give $4x^{2}$ .

Combine both of the terms into one expression to find the answer: $18x^{3}y^{2}+4x^{2}$

Report an Error

Example Question #84 : Polynomial Operations

Simplify the following expression.

$(5c^{2}+5)+(-5c-5)$

Possible Answers:

$5c^{2}-5c$

$5c^{2}-5c+10$

$5c^{2}-5c-25$

Correct answer:

$5c^{2}-5c$

Explanation:

$(5c^{2}+5)+(-5c-5)$

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms to solve.

$5c^{2}$ and -5c have no like terms and cannot be combined with anything.

5 and -5 can be combined however:

5-5=0

This leaves us with $5c^{2}-5c$ .

Report an Error

Example Question #2 : How To Subtract Polynomials

Simplify the following:

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

Possible Answers:

2x^3-2x^2+12x

None of the other answers are correct.

4x^3-2x^3-2x^2+12x

8x^3-2x+16

4x^3-2x(x^2+x-6)

Correct answer:

2x^3-2x^2+12x

Explanation:

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

First, FOIL the two binomials:

4x^3-2x(x^2+x-6)

Then distribute the through the terms in parentheses:

4x^3-2x^3-2x^2+12x

Combine like terms:

2x^3-2x^2+12x

Report an Error

View Algebra 2 Tutors

Nathan
Certified Tutor

California Polytechnic State University, San Luis Obispo, Bachelor, Electrical Engineering.

View Algebra 2 Tutors

Maggie
Certified Tutor

Kalamazoo College, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

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

Popular Subjects

ACT Tutors in Chicago, Reading Tutors in Dallas Fort Worth, Chemistry Tutors in Houston, Reading Tutors in Miami, Math Tutors in Boston, Spanish Tutors in Dallas Fort Worth, Algebra Tutors in Boston, MCAT Tutors in Houston, Physics Tutors in Atlanta, English Tutors in Atlanta

Popular Courses & Classes

Spanish Courses & Classes in San Diego, SAT Courses & Classes in Washington DC, SAT Courses & Classes in Boston, GRE Courses & Classes in Chicago, Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Chicago, MCAT Courses & Classes in Boston, SSAT Courses & Classes in Denver, SAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Seattle

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in Miami, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Chicago, SAT Test Prep in Phoenix, GRE Test Prep in San Francisco-Bay Area, MCAT Test Prep in Seattle, SAT Test Prep in Denver, SSAT Test Prep in Philadelphia, MCAT 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 : Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3 : Monomials

Example Question #51 : Expressions

Example Question #2 : Simplifying Expressions

Example Question #2 : How To Factor A Variable

Example Question #52 : Expressions

Example Question #53 : Expressions

Example Question #54 : Expressions

Example Question #83 : Polynomial Operations

Example Question #84 : Polynomial Operations

Example Question #2 : How To Subtract Polynomials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: