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

- Psychology 316: Advanced Social Psychology
- Hiring & Developing Employees
- Accounting 305: Auditing & Assurance Services
- MTEL Physical Education (22): Study Guide & Test Prep
- Praxis Art - Content Knowledge (5134): Practice & Study Guide
- Victimization at School & the Workplace
- Types of Property Crimes
- The Victim Movement
- Consequences of Crime Victimization
- The Nature of Violence
- Study.com CLEP Scholarship for Military Members
- Study.com Scholarship for Texas Students & Prospective Teachers
- Study.com Scholarship for Florida Students & Prospective Teachers
- What are TExMaT Exams?
- What is the Florida Teacher Certification Examination (FTCE)?
- Study.com TExES Scholarship: Application Form & Information
- Study.com FTCE Scholarship: Application Form & Information

- Children Living in Poverty: Facts, Effects & Statistics
- Reading & Interpreting Bar Graphs
- Specific Intent Crimes: Definition & Examples
- What is DNA Fingerprinting? - Process & Uses
- How to Evaluate International Markets
- Causation of War: Individual, State & System
- The Mesolithic Age in India
- Rural Settlement Pattern Types
- Quiz & Worksheet - Conspiracy in Law
- Quiz & Worksheet - Pantheistic Beliefs & Religions
- Quiz & Worksheet - Spanish Adjectives Starting With S
- Quiz & Worksheet - Benefits to Reflective Practices at Work
- Quiz & Worksheet - Methods of DNA Sequencing
- International Law & Global Issues Flashcards
- Foreign Policy, Defense Policy & Government Flashcards

- Ohio Assessments for Educators - Chemistry: Practice & Study Guide
- Big Ideas Math Common Core 7th Grade: Online Textbook Help
- Middle School Earth Science Curriculum Resource & Lesson Plans
- Astronomy 101 Syllabus Resource & Lesson Plans
- GACE Political Science: Practice & Study Guide
- Theories of Abnormal Psychology Lesson Plans
- Lesson Plans for Calculations, Ratios, Percent & Proportions
- Quiz & Worksheet - What are the Elements of a Crime?
- Quiz & Worksheet - O.J. Simpson Case
- Quiz & Worksheet - Bailment
- Quiz & Worksheet - The Cambodian Genocide
- Quiz & Worksheet - Protist Cell Walls

- Prison Overcrowding: Statistics, Causes & Effects
- Budget Surplus: Definition & Overview
- Globalization & International Management: Assignment 1
- What To Do If Your School Doesn't Accept Study.com Credit
- Professional Resources for Studying Medicine
- Speed Reading for Kids
- Benefits of Study.com vs. Traditional College
- How to Pass the Earth Science Regents Exam
- Business Writing Training
- Best Way to Learn Spanish On Your Own
- How to Pass the RICA
- WIDA Can Do Descriptors for Grade 1

Browse by subject