Back To Course

High School Precalculus: Help and Review32 chapters | 297 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Laura Pennington*

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Trinomials are polynomials with three terms. In this lesson, we'll see how to square a trinomial using a formula and learn how the formula is derived - which gives us another way to square a trinomial!

In mathematics, a **trinomial** is an algebraic expression that has three terms and takes on the form *a* + *b* + *c*. The terms *a*, *b*, and *c* can be numbers, variables, or some combination of the two.

When we square a trinomial, we square it the same way we would any ordinary number or variable: we multiply it by itself.

(*a* + *b* + *c*)2 = (*a* + *b* + *c*)(*a* + *b* + *c*)

Now, before we go any further, it's important to note that (*a* + *b* + *c*)2 â‰ *a*2 + *b*2 + *c*2 - an extremely common error.

Okay, now that we've established that, let's look at how to multiply a trinomial by itself. To square a trinomial, we use the following formula:

(*a* + *b* + *c*)2 = *a*2 + *b*2 + *c*2 + 2(*ab* + *bc* + *ac*)

To square a trinomial, all we have to do is follow these two steps:

- Identify
*a*as the first term in the trinomial,*b*as the second term, and*c*as the third term - Plug
*a*,*b*, and*c*into the formula

For example, suppose we wanted to square the trinomial *x*2 + 3*x* - 4. First, we'll identify the first term as *a* = *x*2, the second term as *b* = 3*x*, and the third term as *c* = -4. Now, we just plug the values into the formula and simplify!

As we said earlier, it's just a matter of multiplying the terms and adding them up.

So, where did this formula come from? Let's take a look at how to derive this formula and, in the process, you may find that you like this pattern for squaring a trinomial better than using the formula itself!

As we said earlier, when we square a trinomial, we are multiplying it by itself:

(*a* + *b* + *c*)2 = (*a* + *b* + *c*)(*a* + *b* + *c*)

Now, to multiply any two algebraic expressions with multiple terms (like a trinomial) together, we follow this pattern:

- Multiply the first term of the first factor by each of the terms in the second factor
- Multiply the second term of the first factor by each of the terms in the second factor
- Continue this pattern for each of the terms in the first factor, then add up all of the products

Let's use this pattern to square a trinomial and rewrite (*a* + *b* + *c*)2 as (*a* + *b* + *c*)(*a* + *b* + *c*):

- Starting with the first term of the first factor,
*a*, multiply*a*by each of the terms in the second factor to get*a*2,*ab*, and*ac*

- Moving onto the second term of the first factor,
*b*, multiply it by each of the terms in the second factor to get*ab*,*b*2, and*bc*

- Moving onto the third term of the first factor,
*c*, multiply it by each of the terms in the second factor to get*ac*,*bc*, and*c*2

- That's all of the terms in the first factor, so now we add the products and simplify:

Let's give this process a try! Let's find (7*x* - 2*y* + *z*)2 without using the formula:

First, we rewrite the problem: (7*x* - 2*y* + *z*)2 = (7*x* - 2*y* + *z*)(7*x* - 2*y* + *z*)

Now, we multiply each term in the first factor, one by one, by each of the terms in the second factor:

Last, we add up all the terms and simplify:

Now that you know the actual process of multiplying out the square of a trinomial and the formula you can use to square a trinomial, it's up to you which process you would like to use.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
11 in chapter 15 of the course:

Back To Course

High School Precalculus: Help and Review32 chapters | 297 lessons

- Terminology of Polynomial Functions 5:57
- How to Evaluate a Polynomial in Function Notation 8:22
- Understanding Basic Polynomial Graphs 9:15
- Finding Intervals of Polynomial Functions 7:16
- Short Run & Long Run Behavior of Polynomials: Definition & Examples 6:05
- How to Graph Cubics, Quartics, Quintics and Beyond 11:14
- Pascal's Triangle: Definition and Use with Polynomials 7:26
- The Binomial Theorem: Defining Expressions 13:35
- Coordinate System in Geometry: Definition & Types
- Solving Quartic Equations
- How to Square a Trinomial 6:03
- How to Use the Distributive Property with Fractions 3:15
- Solving Quadratic Equations by Completing the Square
- Go to Polynomial Functions Basics: Help and Review

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- How to Write a Newspaper Article
- Anthem by Ayn Rand: Book Summary
- Field Hockey: Techniques, Rules & Skills
- What's the Difference Between Polytheism and Monotheism?
- The Very Hungry Bear Literacy Activities
- Totem Pole Project Ideas
- The Worst Day of My Life Ever by Julia Cook Activities
- Quiz & Worksheet - Who, What, When, Where & Why
- Quiz & Worksheet - American Ethnic Groups
- Quiz & Worksheet - Kinds of Color Wheels
- Quiz & Worksheet - Phenol Reactions
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Narrative Essay Topics for Teachers
- Middle School Science Worksheets and Printables

- Business Ethics Syllabus Resource & Lesson Plans
- Human Physiology Study Guide
- General Anthropology for Teachers: Professional Development
- Common Core Math Grade 8 - Functions: Standards
- Financial Accounting Textbook
- Practical Application for Quantitative Analysis
- Reform & Emerging Global Markets
- Quiz & Worksheet - Balanced Chemical Equations
- Quiz & Worksheet - Effects of Eating Too Many Carbohydrates
- Quiz & Worksheet - The Field of Meteorology
- Quiz & Worksheet - Accumulation in the Water Cycle
- Quiz & Worksheet - Bayes Theorem Practice Problems

- Orographic Effect: Definition & Concept
- Graphing Proportional Relationships
- 504 Plans in Colorado
- GED Science: Reading Passages
- National Science Standards for Elementary School
- How Long is the GMAT?
- Nervous System Experiments for Kids
- WV Next Generation Standards for Science
- 2nd Grade Indiana Science Standards
- Tennessee Science Standards
- ELL Services in Illinois
- How to Use the GED Science Prep Course

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject