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Lesson 8: Writing algebraic expressions introduction

# Writing expressions with parentheses

We look at some examples of how certain phrases suggest the need for grouping symbols when we write algebraic expressions. Created by Sal Khan.

## Want to join the conversation?

• hello mr khan i like your website
• If in elementary they taught us that "X" stands for being multiplied, but now they are telling us that we are supposed to use "⋅" then why didn't they always just teach us to use the "⋅" symbol instead of "X".?
• Yo
• Am I the only one who sees "`5` times the difference of `x` and `2`" as `5.|x-2|`?
Because "the difference of `x` and `2`" doesn't seem to show direction of subtraction, doesn't say are we subtracting 2 from x or x from 2, it just says "The difference between them". and the absolute value gives just that.
• There is a difference between 5(x-2) and 5*|x-2|. Try some points to see if they are the same thing. Let x=0. 5(0-2)=-10 and 5|0-2|=10, so they are clearly not the same. The breaking point would be 2. At 2, they are both 0. if x>2, they are the same. However, for x < 2, they diverge and absolute value gives the additive inverse of the correct answer.
• this is like pemdas right
• I shouldn't be in 8th grade and be doing 6th grade problems
(1 vote)
• you should alwsys be looking to improve skills that you are "expected" to know
(1 vote)
• the person who commets to this
is smart!
(1 vote)
• Then I must be the smartest
(1 vote)
• nfcgkewxnbjdw?
jehnbcmkqmxj, ihwdsgywsqok-
bhecjdsdh!!
(1 vote)
• I suppose that to find the difference between x and 2, it's best to use obsolute value, such as |x-2| and |x-2|. Both of these expression are implicitly going to yield the same result.
(1 vote)
• I don't get the part about using the parentheses
(1 vote)
• You have to think of somethings as quantities that go together. if you say difference of x and 2, you have to figure where the - sign goes, so it fills in for the and to get x-2. These go together, so you need the parentheses to show them as going together. If you have 5x-2, it would have to read 5 times x minus to or the difference of 5 times x and 2 (this is similar, but the x and 2 are not linked together in this case, thus the - sign still takes the place of amd, but no parentheses because they are not linked together. Does this help at all?
(1 vote)

## Video transcript

- [Narrator] We have two different statements written in English that I would like you to pause this video and try to write as an algebraic expression. All right, now let's work on this first one. So you might be tempted to say, all right, I have five. So let me just write a five, times and I'll write a dot because when we're dealing with algebra, if you write a traditional multiplication sign, it can get confused with an X. So five times the difference of X and two. The difference of X and two, we could write as X minus two, but this expression has a problem because whoever's interpreting it, if they're following order of operations, which they should, that would mean that they would multiply the five and the X first and then subtract two. But that's not what's going on in the sentence. It's five times, not X, but the difference of X and two. So what you need to do is put parentheses here to make sure that you take the difference of X and two first, and then multiply that by five. Now, with that in mind, let's tackle this example right over here, 10 times the sum of Y and three. Well, once again, if you just wrote 10 times the sum of Y and three, you'll run into the same problem. someone would interpret this as, hey, maybe I should multiply 10 and Y first, because that's what order of operations would tell me to do, but that's not what we want. We want 10 times, not just Y, but the sum of Y and three. So that's where the parentheses are really important to make sure that we take the sum of Y and three first and then multiply that by 10.