Back To Course

High School Trigonometry: Help and Review30 chapters | 228 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn what sets perfect square binomials apart from other trinomials in the math world. You will also learn an easy method to identify them along with a simple procedure to factor them.

A **perfect square binomial** is a trinomial that when factored gives you the square of a binomial. For example, the trinomial *x*^2 + 2*xy* + *y*^2 is a perfect square binomial because it factors to (*x* + *y*)^2. Do you notice how the trinomial in factored form is the square of a binomial? Also, look at the first and last term of the trinomial. Do you notice something interesting about them? Both terms are perfect squares. That is one indication that the trinomial you are dealing with may be a perfect square binomial.

Here are some more examples of special case trinomials that are perfect square binomials.

Do you see a pattern in these trinomials and their respective factored forms? Do you see how these are special trinomials? This is what sets them apart from other trinomials. It actually makes factoring them easier if you know that they are a perfect square binomial before you begin to factor.

An easy way to check whether a trinomial is a perfect square binomial is to look at the first and third term to see if they are perfect squares. If they are, then check the second term by dividing it by 2. The result should be the two perfect squares multiplied by each other.

For example, the trinomial *x*^2 + 2*xy* + *y*^2 has perfect squares for the first and third term. The first term is *x*^2 and the third term is *y*^2. Multiply the two squares together and you get *xy*. When you divide the middle term by 2, you should get *xy*.

Notice the third trinomial in the list and you will see that the middle term is a negative. The middle term can be either positive or negative. The negative sign determines the sign of the factored form.

Once you have identified the trinomial as a perfect square binomial, factoring it becomes very easy. Recall the patterns you saw in the examples. What did you notice about the factored forms of the trinomials? They had the squares as the first and second term. So, factoring a perfect square binomial requires you to know your squares table (1x1=1; 2x2=4; 3x3=9; etc.). If you haven't already memorized them, start reviewing them now.

Look at this factoring example, and see if you can follow the steps.

In the first step, the first and third term of the trinomial are rewritten as perfect squares. In the next step, the middle term is rewritten as the addition of the two identical terms. You can divide the middle term by two to get the two identical terms. These two terms are identified as the multiplication of the perfect squares. Your two perfect squares are 2*x* and 2*y*. When you multiply them together, you get 4*xy*.

Because the trinomial breaks down like this, you know that this is a perfect square binomial and your factored form is the square of a binomial where the first and last terms are your perfect squares from the trinomial. Remember, you keep the sign of the middle term in your factored form. If the middle is negative, then your factored form will have to be a minus.

Try your hand at one more example. See if you can solve it before we go through the steps.

In this example, the middle term is negative, but it can still be broken down into two identical terms, which happen to be the perfect squares multiplied by each other. Do you see how the factored form retains the negative sign?

There is definitely a pattern to perfect square binomials. Because mathematicians like patterns and putting them into formulas, there is a formula for perfect square binomials. It is this:

You can use this formula to multiply out the binomial square or to factor trinomials that are perfect square binomials.

This formula can also be written for a negative middle term like this:

A **perfect square binomial** is a trinomial that when factored gives you the square of a binomial. Not all trinomials are perfect square binomials. Only if the trinomial meets certain criteria can it have such a special label. The criteria include having perfect squares for the first and third terms, and the middle term, when divided by 2, must equal the perfect squares multiplied together. Then and only then is the trinomial a perfect square binomial. Because mathematicians like patterns and putting them into formulas, there is a formula for perfect square binomials. It is this: (*a* + *b*)^2 = *a*^2 + 2*ab* + *b*^2.

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
6 in chapter 22 of the course:

Back To Course

High School Trigonometry: Help and Review30 chapters | 228 lessons

- Trigonometric Ratios and Similarity 6:49
- Practice Finding the Trigonometric Ratios 6:57
- The Pythagorean Theorem: Practice and Application 7:33
- Finding Distance with the Pythagorean Theorem 6:54
- Trigonometry and the Pythagorean Theorem 4:14
- Perfect Square Binomial: Definition & Explanation 4:44
- Special Triangle: Rules & Formulas 3:41
- Tangent in Trigonometry: Definition & Overview
- Tangent Ratio: Definition & Formula 7:05
- Tangents: Definition & Properties
- Triangular Pyramid: Definition, Formula & Examples 5:54
- Calculating Angles for a 5-12-13 Triangle
- Go to Triangle Trigonometry: Help and Review

- C (ASCP) Technologist in Chemistry: Study Guide & Exam Prep
- MLT (ASCP) Medical Laboratory Technician: Study Guide & Exam Prep
- Pennsylvania Grades 4-8 Core Assessment - Mathematics & Science (5155): Study Guide & Test Prep
- Literary Elements Lesson Plans & Resources
- Pennsylvania Grades 4-8 Core Assessment - English Language Arts & Social Studies (5154): Study Guide & Test Prep
- Required Assignments for Business 302
- U.S. Colonial Resistance Lesson Plans
- Common Core Lesson Plan Templates & Resources
- Team Building Lesson Plans & Resources
- Settings in Literature Lesson Plans & Resources
- California Code of Regulations for Schools
- WV Next Generation Standards for Math
- Continuing Education Opportunities for Microbiology Technologists
- Professional Publications in Literacy
- Dyslexia Programs in Texas
- Study.com's Teacher Edition
- Study.com School Plans

- Octahedron: Definition & Properties
- Psychomotor Domain: Definition & Examples
- What is a Paraprofessional Teacher? - Definition & Role
- What is Jazz Dance? - History & Terms
- Complex Number Activities & Games
- Tang Dynasty: Government, Economy & Trade
- Pauropoda: Characteristics, Classification & Examples
- Epstein-Barr Virus Serology: Markers & Interpretation
- Quiz & Worksheet - Background of Massachusetts's Drinking Age
- Quiz & Worksheet - Great Expectations Genre
- Quiz & Worksheet - Test Tubes in Science
- Quiz & Worksheet - Understanding Taboos
- Quiz & Worksheet - Function & Structure of Telomerase
- Graphs & Charts in Everyday Life Flashcards
- Interpreting & Analyzing Data Sets Flashcards

- GACE Biology: Practice & Study Guide
- High School Physics Curriculum Resource & Lesson Plans
- College Algebra Syllabus Resource & Lesson Plans
- College Precalculus Syllabus Resource & Lesson Plans
- ORELA Biology: Practice & Study Guide
- AEPA Middle Grades ELA: Literary Interpretation
- ORELA ELA: English Grammar Conventions
- Quiz & Worksheet - Plane Mirror
- Quiz & Worksheet - Private Brands
- Quiz & Worksheet - Finding a Missing Coin
- Quiz & Worksheet - Life Influences on Cognitive Development in Early Adulthood
- Quiz & Worksheet - Kagan's Research on Temperament in Toddlers

- The Lady of Shalott by Tennyson: Summary, Poem Analysis & Interpretation
- Finding the Limit of (1-cos(x))/x
- Transportation Lesson Plan
- How to Answer NCLEX Questions
- Special Education Resources for Parents
- Sequencing Activities for 3rd Grade
- North Carolina State Standards for Social Studies
- Math Project Rubrics
- Illinois Common Core Social Studies Standards
- Special Education Resources for Parents
- Praxis Tests in Arkansas
- Narrative Writing Rubric Examples

Browse by subject