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Distributing Positive and Negative Signs

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  • 0:01 Distributive Property
  • 0:49 Positive Signs
  • 1:48 Practice Problems
  • 3:17 Negative Signs
  • 4:08 Practice Problems
  • 5:22 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.

It's not just numbers and variables that get distributed. Positive and negative signs can, too. In this lesson, we'll learn how to distribute positive and negative signs correctly.

Distributive Property

The distributive property tells us that a(b + c) = ab + ac. Imagine you're b and you're in a car with your friend c. It's winter and really cold outside. The cold is a. A wants in. It wants to distribute itself throughout the car. And what happens if a door or window opens? A is distributed, and now you're ab and your friend is ac. The cold a has latched itself onto both of you.

So, that's how the distributive property works, at least in cold winter terms. But just as the cold can permeate a previously warm car, other things can distribute, or permeate. In this lesson, we'll learn about two of these distributing forces: positive signs and negative signs.

Positive Signs

A positive sign is like happiness. It's totally, well, positive. Look at this expression: +(x + 1). That positive sign is like a rainbow just itching to get inside. And what does it do if we distribute it? We get x + 1. So, a positive sign makes no difference on the signs.

Really? A rainbow can't turn a frown upside down? It's true. Look at this one: +(2x - 3). That three is feeling kind of down, as we know from the negative sign in front of him. What if we distribute the positive sign? We can imagine the sign is a +1. What's +1 * 2x? 2x. No change there. What about +1 * -3? Still -3. That -3 is really in a funk. So if we simplify +(2x - 3), we get 2x - 3.

Practice Problems

Let's try a couple of practice problems involving positive signs. Here's one: +(3x + 5). We have a positive sign, like bacon. Bacon is awesome! Well, if we try +1 * 3x, we get 3x. And +1 * +5? That's +5. So, our simplified expression is 3x + 5. Sorry, bacon, your charms do nothing here. Maybe our 3x and +5 are vegetarians.

Let's do one more: +(-4 - 9x - 2y). Okay, if -4 and -9x and -2y are in a room together, that's an overwhelmingly negative room. It's like a group of friends watching their favorite football team lose 43 to 8. But then there's that positive sign that wants to get distributed. It's like an adorable kitten at the door. How can that not affect you?

Well, +1 * -4 is, yep, -4. +1 * -9x is -9x. I think you see where this is going. +1 * -2y? That's -2y. So, we can distribute all the adorable kittens we want, we still get -4 - 9x - 2y, with no signs changing. Maybe they're allergic to kittens. Or maybe their football team got beaten by a team inexplicably called the Kittens, so the kitten is a reminder of that pain.

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