Skip to main content
Home
  • Canvas
  • Visit
  • myUNTD
  • Give
  • Apply
  • About Us
    • Why UNTD?
    • Leadership
    • Accreditations
    • Visit Campus
    • News
  • Academics
    • Programs
    • Online Programs
    • Academic Catalog
    • Academic Calendars
    • Academic Affairs
    • College of Law
    • Library
  • Admissions & Aid
    • Undergraduate Admissions
    • Undergraduate Advising
    • Graduate School
    • Financial Aid & Scholarships
    • Registrar
    • Tuition and Fees
    • Trailblazer Elite
  • Our Campus
    • Student Affairs
    • Residence Life
    • Alumni & Friends
    • Police
    • Parking
    • Bookstore
  • Athletics 
  • Resources
    • Student Solutions Center
    • Faculty and Staff Links
    • Veterans
    • Alumni & Friends
    • Human Resources
    • Finance and Administration Services
    • Search Website
    • Office Directory
    • Employee Directory
  1. UNT Dallas
  2. Learning Commons
  3. Science
  4. Algebra
  5. Binomials and FOIL Method
  • Binomials and FOIL Method
  • Exponents and Logarithms

Binomials and FOIL Method

What is a binomial?

A binomial is an algebraic expression of the sum (+) or the difference (-) of two terms.

Quick Review:

Let’s review some terms and expressions that might help us understand these.

Monomial examples: $5y, 8x^2, -2x$

Binomial examples: $-3x^2-2,9y-2y^2$

Polynomial examples: $8x^2+3x-2,12x^2+11x+2$

What is a polynomial?

Polynomials are algebraic expressions that include real numbers (positive, negative, large, small, whole, or decimal numbers) and variables (x, y, etc.). They include more than term and are the sum of monomials. They are usually also written in decreasing order of terms.

 

Term Polynimal or Not? Why?
$8x^2+3x-2$ Polynomial  
$8x^{−3}-7y-2$ NOT a polynomial The exponent is negative ($x^{−3}$)
$8x^2+8x-\frac{2}{3}$ NOT a polynomial Cannot have division

Now...how do we multiply binomials?

When multiplying binomials, you can use the FOIL method. For instance, to find the product of 2 binomials, you’ll add the products of the First terms, the Outer terms, the Inner terms, and the Last terms.

FIRST: multiply the first term in each set of parenthesis

OUTER: multiply the outer term in each set of parenthesis

INNER: multiply the inner term in each set of parenthesis

LAST: multiply the last term in each set of parenthesis

Example 1

Let’s work out this problem.

$$(3x-7)(5x+6)$$

1. Identify the FOIL numbers

\begin{align*}
\color{#FF0000}{\text{First}}&:3x\cdot5x\\
\color{#FF8C00}{\text{Outer}}&:3x\cdot6\\
\color{#008000}{\text{Inner}}&:(−7)\cdot5x\\
\color{black}{\text{Last}}&:(−7)\cdot6\\
\end{align*}

2. Multiply the terms

\begin{align*}
\color{#FF0000}{\text{First}}&:3x\cdot5x=\color{#FF0000}{15x^2}\\
\color{#FF8C00}{\text{Outer}}&:3x\cdot6=\color{#FF8C00}{18x}\\
\color{#008000}{\text{Inner}}&:(−7)\cdot5x=\color{#008000}{−35x}\\
\color{black}{\text{Last}}&:(−7)\cdot6=\color{black}{−42}\\
\end{align*}

3. Combine like terms

\begin{align*}
$\color{#FF8C00} {18x} \color{#008000} {−35x}= {−17x}
\end{align*}

4. Combine all terms in decreasing order

\begin{align*}
$\color{#FF0000} {15x^2} \color{#FF8C00} {−17x} \color{black} {−42}
\end{align*}

Final Answer: $$15x^2-17x-42$$

Example 2

$$(5+4x)(3+2x)$$

$$(5+4x)(3+2x)$$

$$= \color{#FF0000}{(5\cdot3)} + \color{#FF8C00}{(5\cdot2x)} + \color{#008000}{(4x\cdot3)} + \color{black}{(4x\cdot2x)}$$

$$= \color{#FF0000}{15} + \color{#FF8C00}{10x} + \color{#008000}{12x} + \color{black}{8x^2}$$

$$= \color{#FF0000}{15} + \color{#FF8C00}{22x}+ \color{black}{8x^2}$$

$$= \color{black}{8x^2}+ \color{#FF8C00}{22x}+ \color{#FF0000}{15}$$

Final answer: $$8x^2+22x+15$$

Additional Resources

Our Math Tutors recommend the following websites for help:

Paul's Online Notes: Polynomials 

 

Quick Links

  • Employment
  • Directory
  • Syllabi and CV (HB2504)
  • University Policies

Help and Safety

  • Report Concern For A Student
  • Title IX Resources
  • Disability Services
  • Employee Mental Health
  • Student Mental Health

Info Center

  • Information Technology
  • Marketing and Communications
  • Book an Event On Campus

UNT System

  • UNT Dallas President
  • UNT President
  • UNTHSC President
  • UNT System Chancellor
Home
7300 University Hills Blvd
Dallas, Texas 75241
FacebookInstagramTwitterLinkedInYouTube

Footer Links 1

  • AA/EOE/ADA
  • Disclaimer
  • Electronic Accessibility
  • Notice of Non-Discrimination
  • Privacy

Footer Links 2

  • Campus Carry
  • Clery Act
  • Compliance Trust Line
  • Requests for Public Information
  • Student Complaint Process

Footer Links 3

  • Accreditation Statements
  • Institutional Finance (51.9741)
  • Institutional Resume
  • Report Fraud, Waste or Abuse
  • Statewide Search

Footer Links 4

  • Compact with Texas
  • Texas.gov
  • Texas Homeland Security
  • Texas Veterans Portal
© 2023 University of North Texas at Dallas
Back To Top
©