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Lesson 5: The distributive property & equivalent expressions

# Combining like terms with negative coefficients & distribution

We've learned about order of operations and combining like terms. Let's layer the distributive property on top of this. Created by Sal Khan.

## Want to join the conversation?

• What is the key to getting the answer to problems like these? I get lost so fast!
• The key realization here is to realize that we can't combine things that are different from one another. And you must also learn or master how to distribute so you can solve these problems
I know this is probably not such a good example, I'll improve my example as soon as I can think of a better one.
For instance we have 3 oranges and 8 apples, in all we have 11 fruits. let o=oranges, a=apples, f=fruits
Mathematically we can say that 3o+8a=11f
But we know that oranges and apples are both fruits so
3f+8f=11f
• I'm slightly confused, in the second example it says 7(3y - 5) - 2 (10 + 4 y), but he simplifies the last parentheses as -20 -8y......What happened to the plus symbol during the simplification?
• emassingill1,

Sal distributed the -2 over the quantity in the second parenthesis. In other words he multiplied -2 * (10 +4y), which you do by multiplying the -2 times EVERYTHING in the parentheses. So -2*10=-20 and -2*4y=-8y. Adding those together yields:
-20+ -8y = -20-8y.
• What is it called when you replace a number for a letter
• When you replace a number with a letter the letter is called a variable. Variables can be used to figure out questions like " If sally used 4 stars for a painting how many would she need for 79 paintings? Write an expression.
Number of painings: x
stars:y
X4=y

Hope this helped!
• bring back chuck norris
• At to , how come he did not do the inverse of that operational sign when it comes to subtracting 21y - 35 - 20 - 8y if the operation of the 8y is negative?
• Leah,
21y-35-20-8y is the same thing as
21y + (-35) +(-20) +(-8y)
and addition is commutative so we can chage the order to
21y +(-8y) + (-35) +(-20) Now the 21y + -8y is 13y for the same reason that 21 apples miuns 8 apples is 13 apples, so
13y + (-35) +(-20) Now the -35 and -20 can be added to be -55 so

I hope that helps make it click for you.
• I liked the Chuck Norris
• I'm kind of confused, in the second example it says 7(3y - 5) - 2 (10 + 4 y), but Sal simplifies the last parentheses as -20 -8y so I am confused What happened to the plus symbol during the simplification?
• A negative multiplied by a positive results in a negative. When you multiply -2 by 4y, the answer will be -8y.
• not chuck norris :0

how could he get rid of chuck Norris ToT
• A lot of people were very "surprised" when they saw Chuck Norris on the last video. So maybe that's why.
• Bro, Sal's mouse skills are crazy! I can't even draw a minus symbol straight!
• Sal uses a tablet with a stylus rather than a mouse. This is why he writes so well.