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Lesson 2: The distributive property & equivalent expressions

# Equivalent expressions: negative numbers & distribution

Learn how to identify equivalent expressions using your knowledge of the distributive property and negative numbers.

## Want to join the conversation?

• This has been bothering me for ages, and a thanks to Sal Khan for answering my other 24(maybe it was 240, I'm not sure)...but I still have one question...

1. I'm not sure if this appeals to THIS video... But it's related. Sometimes Sal changes a negative into a minus sign... How is that possible?

Any and all help will be appreciated,

• It would have been a + -12, so instead he just made it -12, as they are the exact same.
• I am confused when I use this in word problems.
• 5 Years Later...
I know how you feel. Believe me, when I just started, I thought I'd be old and gray before I finished! But when you get used to them, it actually isn't that hard.
• it sort of helps but im still confused
• Here's a tip: Start out by doing what's in the parenthesis. Then follow the rest of the rules in PEMDAS. If you still need help, just ask and I will help you with the problem.
• how do you do it if it is a negative minus aa number times a positive minus three
example -c-6(2c-6)
• Hi again!

Yes! we can multiply unlike terms.

We can multiply the coefficients, then place the variables together, behind and against our new coefficient.

2x • 5y = 10xy

Why? The concepts in action

The coefficient is the number that is smooshed in front of a variable, the coefficient is the count of that variable's repeats combined, so it represents the number of times the variable occurs.)

(x + x) • (y + y + y + y + y)
=
2x • 5y

So…
★ That's one of the reasons we can multiply Unlike Terms is because the relationship between the coefficient and the variable is Multiplication!
Let's take a closer look…

2x • 5y
=
2 • x • 5 • y

Another reason we can is the useful Property of Multiplication, (a truth about it), it's Commutative (interchangeable), which means we can rearrange multiplication terms, and still get the same answer!
4 • 3 • 2 = 24 = 2 • 4 • 3 = 24

Which is what we're doing (when we multiply unlike terms), just rearranging a multiplication expression, by completing the calculation for the values we do know (the coefficients), and keeping the unknown values (variables) set up properly to multiply!

2x • 5y
=
2 • x • 5 • y
=
2 • 5 • x • y
=
10 • x • y
=
10xy ←yay! 🥳

So that's why when multiplying unlike terms, we can just multiply the coefficients, and tack the variables on at the end!

It works when there are exponents >1 as well, but take note of addition or subtraction operations zones, they act like barriers for the multiplication, only cross them after you complete the multiplication and only if you can combine like terms!

2ab • 4w^2 + 5x • 3y - z^2 • 5u
=
(2ab • 4w^2) + (5x • 3y) - (z^2 • 5u)
=
8abw^2 + 15xy - 5uz^2 ←yay! 🥳

We rarely need to show all the details, but knowing and understanding the 'how' and 'why' of 'what' is happening can help us take the next step up in comprehension!

I hope this helps someone! (≧▽≦)
• does anyone else speed the videos x2
• 1x1=1, ok now we will explain what that algebraically means in a 30 minute video
• TO ANY ONE WHO IS CONFUSED ON THE DIFFERENCE BETWEEN TERMS AND EXPRESSIONS, I CAN HELP OUT:
Hey guys, HotCocoa here! I had trouble with this at first, too.
Expressions are like this simple one: 2+4, or -3 + (5 x 8v) x 29v. You see, it doesn't have an equal sign, it doesn't have an answer, it's not meant to be solved. now, an EQUATION is meant to be solved, like this: 99-37=?
Please like if this helped you, and comment if you have any more questions or want to add on or give me feedback.
Happy to help :)
• i love kahn academy and i appreciate the help but sometimes... i think sal took a knife to my brain with this math stuff.
• khan academy is a a good site and i'm definitley not being forced to say this