Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Algebra : Polynomial Identities and Numerical Relationships: CCSS.Math.Content.HSA-APR.C.4

Study concepts, example questions & explanations for Common Core: High School - Algebra

Create An Account

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 10 b\right)^{2}$

Possible Answers:

$10 a b + 100 b^{2}$

$a^{2} + 20 a b + 100 b^{2}$

$b^{2}$

$a^{2} + 20 a b$

$a^{2}$

Correct answer:

$a^{2} + 20 a b + 100 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 10 b\right)^{2} = \left( a + 10*b \right) \cdot \left( a + 10*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 10 b = 10 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 10 b = 10 a b$

Now we multiply the last terms of each expression together.

$10 b \cdot 10 b = 100 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 20 a b + 100 b^{2}$

Report an Error

Example Question #2 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 14 b\right)^{2}$

Possible Answers:

$14 a b + 196 b^{2}$

$a^{2} + 28 a b$

$a^{2} + 28 a b + 196 b^{2}$

$a^{2}$

$b^{2}$

Correct answer:

$a^{2} + 28 a b + 196 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 14 b\right)^{2} = \left( a + 14*b \right) \cdot \left( a + 14*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 14 b = 14 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 14 b = 14 a b$

Now we multiply the last terms of each expression together.

$14 b \cdot 14 b = 196 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 28 a b + 196 b^{2}$

Report an Error

Example Question #3 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 2 b\right)^{2}$

Possible Answers:

$2 a b + 4 b^{2}$

$a^{2}$

$a^{2} + 4 a b$

$a^{2} + 4 a b + 4 b^{2}$

$b^{2}$

Correct answer:

$a^{2} + 4 a b + 4 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 2 b\right)^{2} = \left( a + 2*b \right) \cdot \left( a + 2*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 2 b = 2 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 2 b = 2 a b$

Now we multiply the last terms of each expression together.

$2 b \cdot 2 b = 4 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 4 a b + 4 b^{2}$

Report an Error

Example Question #1 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 17 b\right)^{2}$

Possible Answers:

$a^{2}$

$a^{2} + 34 a b$

$17 a b + 289 b^{2}$

$a^{2} + 34 a b + 289 b^{2}$

$b^{2}$

Correct answer:

$a^{2} + 34 a b + 289 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 17 b\right)^{2} = \left( a + 17*b \right) \cdot \left( a + 17*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 17 b = 17 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 17 b = 17 a b$

Now we multiply the last terms of each expression together.

$17 b \cdot 17 b = 289 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 34 a b + 289 b^{2}$

Report an Error

Example Question #4 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 3 b\right)^{2}$

Possible Answers:

$3 a b + 9 b^{2}$

$b^{2}$

$a^{2} + 6 a b$

$a^{2}$

$a^{2} + 6 a b + 9 b^{2}$

Correct answer:

$a^{2} + 6 a b + 9 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 3 b\right)^{2} = \left( a + 3*b \right) \cdot \left( a + 3*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 3 b = 3 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 3 b = 3 a b$

Now we multiply the last terms of each expression together.

$3 b \cdot 3 b = 9 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 6 a b + 9 b^{2}$

Report an Error

Example Question #2 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 2 b\right)^{2}$

Possible Answers:

$a^{2} + 4 a b$

$b^{2}$

$2 a b + 4 b^{2}$

$a^{2}$

$a^{2} + 4 a b + 4 b^{2}$

Correct answer:

$a^{2} + 4 a b + 4 b^{2}$

Explanation:

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 2 b = 2 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 2 b = 2 a b$

Now we multiply the last terms of each expression together.

$2 b \cdot 2 b = 4 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 4 a b + 4 b^{2}$

Report an Error

Example Question #3 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 15 b\right)^{2}$

Possible Answers:

$a^{2}$

$a^{2} + 30 a b + 225 b^{2}$

$a^{2} + 30 a b$

$15 a b + 225 b^{2}$

$b^{2}$

Correct answer:

$a^{2} + 30 a b + 225 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 15 b\right)^{2} = \left( a + 15*b \right) \cdot \left( a + 15*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 15 b = 15 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 15 b = 15 a b$

Now we multiply the last terms of each expression together.

$15 b \cdot 15 b = 225 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 30 a b + 225 b^{2}$

Report an Error

Example Question #242 : High School: Algebra

Use FOIL for the following expression.

$\left(a + 7 b\right)^{2}$

Possible Answers:

$a^{2} + 14 a b + 49 b^{2}$

$a^{2}$

$7 a b + 49 b^{2}$

$b^{2}$

$a^{2} + 14 a b$

Correct answer:

$a^{2} + 14 a b + 49 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 7 b\right)^{2} = \left( a + 7*b \right) \cdot \left( a + 7*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 7 b = 7 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 7 b = 7 a b$

Now we multiply the last terms of each expression together.

$7 b \cdot 7 b = 49 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 14 a b + 49 b^{2}$

Report an Error

Example Question #5 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 6 b\right)^{2}$

Possible Answers:

$a^{2}$

$b^{2}$

$6 a b + 36 b^{2}$

$a^{2} + 12 a b + 36 b^{2}$

$a^{2} + 12 a b$

Correct answer:

$a^{2} + 12 a b + 36 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 6 b\right)^{2} = \left( a + 6*b \right) \cdot \left( a + 6*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 6 b = 6 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 6 b = 6 a b$

Now we multiply the last terms of each expression together.

$6 b \cdot 6 b = 36 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 12 a b + 36 b^{2}$

Report an Error

Example Question #7 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 5 b\right)^{2}$

Possible Answers:

$a^{2}$

$\ a^{2} + 10 a b$

$b^{2}$

$a^{2} + 10 a b + 25 b^{2}$

$5 a b + 25 b^{2}$

Correct answer:

$a^{2} + 10 a b + 25 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 5 b\right)^{2} = \left( a + 5*b \right) \cdot \left( a + 5*b \right)$

Now we multiply the first parts of the first and second expression together.

$a \cdot a = a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a \cdot 5 b = 5 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a \cdot 5 b = 5 a b$

Now we multiply the last terms of each expression together.

$5 b \cdot 5 b = 25 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 10 a b + 25 b^{2}$

Report an Error

View Tutors

Edmund
Certified Tutor

University of Ghana, Bachelor of Science, Statistics. university of Ghana, Master of Philosophy, Statistics.

View Tutors

Muddasir
Certified Tutor

National University of Science and Technology (NUST), Bachelor, Electrical Engineering.

View Tutors

Alvin
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Computer Science.

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Boston, Physics Tutors in Boston, French Tutors in Boston, ISEE Tutors in Chicago, Statistics Tutors in Los Angeles, Computer Science Tutors in Boston, English Tutors in Miami, Calculus Tutors in Dallas Fort Worth, Math Tutors in Seattle, SSAT Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Philadelphia, ACT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Seattle, SSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Seattle, ISEE Courses & Classes in San Diego, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Chicago, MCAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Miami, GRE Test Prep in Philadelphia, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in New York City, SSAT Test Prep in Houston, LSAT Test Prep in Denver, GRE Test Prep in Atlanta

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

Common Core: High School - Algebra : Polynomial Identities and Numerical Relationships: CCSS.Math.Content.HSA-APR.C.4

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #1 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #2 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #3 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #1 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #4 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #2 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #3 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #242 : High School: Algebra

Example Question #5 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #7 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

All Common Core: High School - Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: