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Why Do We Distribute in Algebra? - Explanation & Examples

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  • 0:02 Distribution
  • 1:18 Basic Example
  • 2:00 Two Variables
  • 2:58 Three Variables
  • 4:28 Distributing a Variable
  • 5:08 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

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

What's the purpose of distribution in algebra? In this lesson, we'll find out why we distribute. We'll also look at examples and sample problems that involve basic distribution.

Distribution

Tommy loves to chew gum. He always has a pack of gum in his pocket, much to the dismay of his parents, who sometimes discover it in the wash.

At school, Tommy isn't supposed to chew gum in most classes. But his algebra teacher, Mr. Adams, is cool with it. Mr. Adams tells Tommy he can chew gum in class as long as he brings enough for everyone. He needs to distribute his gum to his algebra classmates.

What does that mean? That means that Tommy takes that pack of gum in his pocket and hands out a piece to everyone, even Mr. Adams. This distribution of gum is just like the distribution they're learning about in algebra, only with more spearmint freshness, more loud gum snapping, and more than a few pieces of gum ending up decorating the desks and chairs.

In algebra, distribution means to spread out terms equally across an expression. We refer to what we're doing as the distributive property, which can be defined as a(b + c) = ab + ac.

Why do we distribute? It's a way of simplifying expressions. This can make them easier to work with. If Tommy shares his gum with his class, more gum chewing can happen. Likewise, if we distribute the a across the parentheses, we've made our expression simpler, and when distribution is part of a larger equation, we can do more with it.

Basic Example

Here's an expression: 6(x + 2). x and 2 are like students in the class, wishing they had some of that gum. Maybe they had salami for lunch. The 6 is like the pack of gum. We want to distribute it to each of the terms inside the parentheses equally.

To do that, we take the 6 and multiply it by each term. So 6 * x = 6x, and 6 * 2 = 12. The only operator we have is that plus sign, so we end up with 6x + 12. This is our simplified expression. See how much happier our x and 2 are? They're quite literally 6 times happier; plus, no worries about grossing out the cute girl in English class.

Two Variables

What if we have an expression like this: 3(2x + y)? This is a class with two variables. I think a variable in a class is that kid who might be a class clown one day and then sit quietly in the back the next day. He's variable; we just don't know. And a class with two variables? That's a recipe for disaster.

But it doesn't change how we distribute. We still take the number outside the parentheses and distribute it, or multiply it, with the terms inside the parentheses. So, 3(2x + y) becomes 3 * 2x and 3 * y.

  • 3 * 2x = 6x
  • 3 * y is just 3y

So, our simplified expression is 6x + 3y. Notice that we can't simplify this any further. We can't add the x and y, so this is as far as we go. It's like cutting up a birthday cake that someone brings to share. You can only cut the slices so small before they're not so much pieces of cake as just crumbs, and then everybody gets sad.

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