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## Get ready for Algebra 1

### Course: Get ready for Algebra 1>Unit 1

Lesson 7: Combining like terms

# Combining like terms with negative coefficients

This example of combining like terms in an expression get a little hairy. Pay attention. Created by Sal Khan.

## Want to join the conversation?

• So x's cannot be combined with xy's or with x^2's, and y's cannot be combined with xy's or with y^2's, right? Doesn't this leave your equation containing a lot of terms still? Wouldn't it be a lot simpler if we could reduce the number of terms more? •   The way I think about it, if x = Turkey and y = farm, then 2 x (Turkeys) are not 3y (Farms) and close but not quite 4xy (Turkey Farms) xy. I just went back to the earlier videos and substituted variables for objects to make myself understand it.
• How do you recognize the difference between the 'minus' sign and the 'negative' sign.
I'm so confused •   Think of them as being the same thing, it is one or the other based on where it is in the equation. The negative sign is used at the beginning of something new, so it could be primarily in three places -3(-4 + x)/-6. A negative is beginning of an expression, the beginning of a parentheses, and the beginning of the denominator. A minus is between things such as 3(2x - 5) - 5(4x - 2) . In this case, it is between an x and a constant and between two expressions. In this case, if you try to distribute -5(4x-2) independently, the minus now is at the beginning and so it is considered a negative sign rather than the minus it was in the full expression. Does this help?
• I have been having trouble understand the -5+6=? I don't understand last video he had two numbers with - signs and he added them and kept the sign why? What am I missing maybe video that could help it seems so simple but I have no clue! Any feed back will be welcomed. •   I think the easiest way to understand this is via the number line.
When we add we move to the right along the number line, and when we subtract we move to the left.
Starting at 0 (zero) we move 5 steps to the left and from there we move 6 steps to the right.

` −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 `
`−−+−−+−−+−−+−−+−−+−−+−−+−−+−−+−−+−−+−−+−−+−−+−−`
` <−−−−( −5 )−−−−− `
` −−−−−−( +6 )−−−−−−> `

As you can see, this lands us at 1.
So, −5 + 6 = 1

– – –

Adding two negative numbers, for example (−3) + (−4), is the same as (from 0) moving 3 steps to the left and then another 4 steps to the left, in total 7 steps to the left, which lands us on (−7),
and we write −3 − 4 = −(3 + 4) = −7

– – –

Sal explains it more thoroughly here:
• at why did he leave out the y2 shouldn't that count as a y to? • can you guys pls upvote and comment i need achievements • At 0.21, what is the difference between x^2 and 2x? • this is confusing.
why don't you just give us the value of x and y so then I can solve it? • You won't always know the values of the variables. Part of learning algebra is that you need to learn the rules for how to manipulate algebraic expression that contain variables. This video is trying to teach one of those techniques. It is a basic skill you need to understand before you start solving algebria equations where you will actual discover for yourself what value the variable can be.
• Sal can you PLEASE tell me what we are supposed to use our Energy Points for?! • Is there any reason why this, [X+2*(X)] + [Y-1*(Y)] , wouldn't work as the answer?
My logic here is that X^2 and Y^2 are equal to X*(X) and Y*(Y) meaning they could be combined with -1*(Y) and 2*(X). • HELP?
On some examples it shows that we move the numbers on the other side of the equal = sign... I get that once thats done the numbers either become a negative or positive but... how do we know when to use it. There's some questions I can solve using the same method in this video but then there's this eg:
-3n - 7 + (-6n) + 1
If I were to use the method above would it be written as so?
-3n - (-6n) -7 + 1 ?
In this equation they used
-3n - 7 + (-6n) + 1
= (3+6)n -7 +1
I don't get it? which method do we use? if both... how are we supposed to know which one is right? or when to use either one? Please. 