Back To Course

ELM: CSU Math Study Guide16 chapters | 140 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 70,000 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:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.

What do you think of when you hear the term 'distribution center'? I think of the mail. When you mail a letter or a package, you might bring it to the post office or put in a mailbox. People all over your town are doing the same thing. All the items from your town get collected and go to a distribution center.

Once they're there, they get sorted and distributed into different trucks depending on where they're going. Then they leave the distribution center and head off to other parts of your town, your state, or even other parts of the world.

The distribution center is the place where everything is organized into logical groups. All the mail for Wyoming goes in one place, and all the mail for Japan goes in another. And this is essentially what the distributive property is all about.

The **distributive property** is a handy math rule that says when you are multiplying a term by terms that are being parenthetically added, you can distribute the multiplication across both terms, then sum their products.

That was totally confusing, I know. The distributive property is much easier to show, and it's much simpler than it sounds. Think of it this way: *a*(*b* + *c*) = (*ab*) + (*ac*).

Let's prove it with real numbers. If we have 5(3 + 4), the order of operations tells us we start with the parenthesis. So we do 3 + 4 = 7, get 5(7) and then end up with 35. That's all well and good. But the distributive property tells us that in this situation, we can instead do (5 * 3) + (5 * 4), where we distribute the 5 across the parenthesis. Does it work? We get 15 + 20. Is that still 35? Yep. It is.

For most purposes, the distributive property is limited to multiplication. And while I said that the parenthetical terms must involve addition, remember that something like (7 - 2) is really just (7 + (-2)), so this rule still works.

If you're wondering why (5 * 3) + (5 * 4) is in any way easier than 5(7), well, it isn't really. It would help to look at some examples of when this is particularly helpful.

What if you can't add what's inside the parentheses? Look at this one: 7(3*x* + 5*y*). You can't simplify 3*x* + 5*y*. But you can distribute the 7 and get 21*x* + 35*y*. In fact, that's when you'll most often use this rule - when you have variables.

Here's another one: -5(6 + 2*x*) Don't forget that negative sign. If we distribute the -5, we get -5 * 6, which is -30, and -5 * 2*x*, which is -10*x*. Put that together and our simplified expression is -30 - 10*x*.

Here's one with a minus sign inside the parenthesis: 4*a*(6 - 2*a*). Remember, 6 - 2*a* is really just 6 + (-2*a*), so our two terms are 6 and -2*a*. 4*a* * 6 is 24*a*. And 4*a* * -2*a* is -8*a*^2. So our simplified expression is 24*a* - 8*a*^2.

Let's try one that's a little more complicated: -2*x*(*x* - 8*y*). Again, pay attention to those negative signs. -2*x* * *x* is just -2*x*^2. Okay, that's not so bad. And -2*x* * 8*y*? Wait - remember, it's -8*y*. Okay, -2*x* * -8*y*. You can't add *x* + *y*, but you can multiply them. We get positive 16*xy*. So our simplified expression is -2*x*^2 + 16*xy*.

How about one more? -(5*a* - 3*b*). What's that negative sign hanging out in front of the parenthesis? It's really a -1. So we need to distribute the -1 across the terms. -1* 5*a* is -5*a*. And -1 * -3*b* is positive 3*b*. So our simplified expression is -5*a* + 3*b*.

In summary, the distributive property can be expressed as *a*(*b* + *c*) = (*ab*) + (*ac*). All we're doing is distributing the *a* across the terms inside the parenthesis. This is especially useful when we're dealing with variables that can't be added. The distributive property gives us the power to simplify our expression.

When this lesson is finished, you should be able to utilize the distributive property when solving algebraic expressions that require multiplication.

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
5 in chapter 6 of the course:

Back To Course

ELM: CSU Math Study Guide16 chapters | 140 lessons

- What is a Variable in Algebra? 5:26
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- The Commutative and Associative Properties and Algebraic Expressions 6:06
- The Distributive Property and Algebraic Expressions 5:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Go to ELM Test - Algebra: Basic Expressions

- Leadership in Action for Coaches
- Introduction to the Internet of Things
- Adaptive Leadership for Agile Organizations
- Chemistry 112: Chemistry II
- Leadership in Action
- Additional CLEP Principles of Macroeconomics Flashcards
- Additional CLEP Analyzing & Interpreting Literature Flashcards
- Additional CLEP History of the United States I Flashcards
- Additional CLEP Information Systems Flashcards
- CLEP Introductory Psychology Exam Flashcards
- Average AFQT Scores
- ASVAB Test Day Preparation
- How To Pass the GED Reading Test
- What is the AFQT?
- What is the Highest ASVAB Score?
- ASVAB Scores for Marines
- Can You Retake the ASVAB?

- Irony & Satire in Great Expectations
- History of Drawing Materials & Techniques
- Tree Diagrams, Sample Space Diagrams & Tables of Outcomes
- How to Create Meaning in Art: Techniques & Examples
- Geography Tools: Fieldwork, Databases & Primary Sources
- Common Drug-Disease Interactions
- Practical Application: Determining Precipitates
- How to Implement Greentailing in Organizations
- Quiz & Worksheet - Questions on The Odyssey Book 22
- Quiz & Worksheet - Confidence Intervals
- Quiz & Worksheet - Vocabulary for Painting Materials & Processes
- Quiz & Worksheet - Sculpting Materials & Techniques
- Quiz & Worksheet - Problems & Solutions When Making Visual Art
- Introduction to Research Methods in Psychology Flashcards
- Clinical Assessment in Psychology Flashcards

- Praxis Social Studies - Content Knowledge (5081): Study Guide & Practice
- Prentice Hall America: History of our Nation: Online Textbook Help
- AP English Language Textbook
- Statistics for Teachers: Professional Development
- Prentice Hall Conceptual Physics: Online Textbook Help
- Square Roots: Tutoring Solution
- Somatoform Disorders in Abnormal Psychology: Help and Review
- Quiz & Worksheet - Impairment, Disability, Developmental Delay & Handicap
- Quiz & Worksheet - Characteristics of Internet Marketing
- Quiz & Worksheet - Sui, Tang & Song Dynasties of China
- Quiz & Worksheet - Post WWII Conflicts in the Middle East
- Quiz & Worksheet - Technology's Impact on Cultures in the Global Age

- The Marketing Mix & Wholesaler Decisions
- Tremolo: Definition & Effect
- Solar System Project Ideas
- How to Pass the TOEFL Exam
- What Do You Learn in Computer Science?
- What Is Science? - Lesson Plan
- The New SAT Score Conversion
- Common Sense Lesson Plan
- DNA Model Project Ideas
- A Rose for Emily Lesson Plan
- Adding & Subtracting Fractions Lesson Plan
- Context Clues Lesson Plan

Browse by subject