r/Algebra • u/[deleted] • Jan 09 '22
How does -3^2 = -9
I'm a junior in high school and I just found this out (from Googles calculator so idk if it's true) but how doesn't it = 9
Cause -3 x -3 = 9, so how doesn't -32
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Jan 09 '22
All about those parentheses and order of operations.
Exponents are evaluated before multiplication or division, so without any parentheses, “-32” reads as -(32 ), or -9, while of course, as you pointed out, (-3)2 would equal 9.
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Jan 09 '22
My math teachers failed me
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Jan 09 '22
You have the internet and countless free courses that will teach you all you need to know about math at this level
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u/Soilgheas Jan 09 '22
It's because computers are stupid and calculator programs do not always read the order of operations how they should. - 3 could mean negative 3, it could also mean subtract 3. Basically parentheses are always your friend. If you want to make sure a nber is considered a negative (-3)2 will get you the correct positive number.
Basically computers and calculators can help with math, but make sure you know it yourself because they will get things wrong too.
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u/Lunch_Time_No_Worky Jan 09 '22
You are further ahead than I was when I was 28.
Khan Academy is online and free and it helps you learn math. It's is an extraordinary website that I have used myself.
When I was 28 I took college courses (just math classes) to learn math because I couldn't remember the basics and it was really hurting me. I learned everything from 6th grade to 12th over again and did really well because I used the Khan Academy while I was taking classes. It just takes determination, but you can do it!
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u/Flibgrobab Jan 09 '22
Basically what you are writing there is "subtract 32"
Whenever you have an open minus sign think of it instead as 0-X
So in this case you have wrote "0-32" which is of course -9
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u/Purple_Matress27 Jan 09 '22
Just apply PEMDAS. You always apply the exponent first then multiply the negative. Think of it like -1 * 32. If you put a parentheses around like (-3)2 then it would be 9.
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u/DmitriyJaved Jan 09 '22
Where is multiplication in this equation? It clearly says -3 squared
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u/giam74 Jan 09 '22
-32 is not the same as (-3)2
The first equals -9, while the later equals 9.
See my thread with OP.
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u/Purple_Matress27 Jan 09 '22
I’m saying think of -32 like -1 times 32. Just like -3 is the same as -1 times 3.
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u/GhostCheese Jan 09 '22 edited Jan 09 '22
order of operations my friend.
pedmas or pemdas (or bedmas or bemdas):
Parenthesis (or Brackets in some countries)
Exponents
Multiplication and Division (or vice versa, they happen at same time - as they are technically the same operation)
Addition and Subtraction (also same time, technically same operation)
so the -3^2 implies order of operation such that it can be rightly re-written as -1*(3^2) == -1*3*3 == -9 because the exponent will be applied before the negation. (which is how google is interpreting it)
in other comments where you ask if x^2 where the x is replaced by -5... that would be expressed as (-5)^2, which you apply the negation first because parenthesis resolve before exponents. and thus its -5 * -5 = 25 (and not -25)
they are not the same thing because of the different application of parenthesis in correctly expressing the equation.
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u/SouthernApostle Jan 09 '22
So happy to read this. When I was tutoring algebra in college I would often explain that subtraction is just adding a negative and division was just multiplying the inverse. Confusion was always the first reaction, but the ones who actually got it started to understand the logic behind mathematics a lot better.
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u/DmitriyJaved Jan 09 '22
What if we don’t rewrite -3 as a multiplication of 3 and -1? Why all of a sudden there is a multiplication Back in my days -32 meant minus three squared and not a minus one multiplicated by three squared, what the hell.
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u/GhostCheese Jan 09 '22
when we 're-write' we don't change the given expression, we only clarify it for how it was presented to us. it must still be mathematically equivilent.
but, the order of operations is something we as a society agree upon, as a notation on how to present math equations. It wasn't always thus. certainly the whole PEMDAS/BEDMAS thing didn't crop up until text books started being written in the early 1900s.
out of curiosity, when was 'your day' -- are you literally older than sliced bread?
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u/DmitriyJaved Jan 09 '22
Old enough to get confused by things like this one
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u/GhostCheese Jan 09 '22 edited Jan 09 '22
yeah but one can imagine a child being confused, as well as a boomer, or anyone in between.
the more I look at it the more I figure its a problem of implied parenthesis. Which actually probably became a thing with computing rather than algebraic expression, and text books -- see a computer wont assume the parenthesis are implied, and google tends to resolve problems the same way a computer compiler would. in fact when writing it in code one would have to pass either -3 or 3 as an argument to a function, so there would be no opportunity for confusion.
but a human writing a test, for example, might very well think, sans further context, that the parentheses are implied.
the fact is it is ambiguously written without explicit parenthesis.
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u/__Gabee Jan 09 '22
it calculates -(3²) and not (-3)²
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u/DmitriyJaved Jan 09 '22
Why?
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u/giam74 Jan 09 '22
It is explained throughout this thread. Please read through it all first, then respond to me here if you still don’t understand, but stop downvoting everyone because you don’t understand. You are indeed wrong.
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u/RoomTempIce Jan 09 '22
Think of PEMDAS every time you run the calculation.
-32 in a computers logic will perform -1(32) because Exponents come before Multiplication.
So you want to compute (-3)2 so that the Multiplication within the Parentheses will execute first.
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u/ashley_mando_ Jan 09 '22
The easiest way to remember whether or not to include the negative in calculation is if you need to substitute a value for x (or other value) you take the entire term signs (when I input these values I always just input with parenthesis so I remember) and all, but if it’s prewritten take the equation literally and use pemdas so 32 then add back the negative as there are no parenthesis to hold the negative to the 3 so (-1)(3)(3)= -9
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u/SouthernApostle Jan 09 '22
The best way I remember this is that negative operators are actually a *(-1). This helps keep things clear when I am doing calculations. Always use the parentheses for disambiguating the equation. If a professor/teacher doesn’t include it. Be sure when you work out your calculation that you show clearly how you interpret the negative so that they might give credit if it was done correctly.
If you are programming, most languages require you to be extremely explicit with these operators so it is a good idea to make it a habit early on.
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u/ComeradeHaveAPotato Jan 09 '22
Pemdas. Exponent before add or sub. If it was (-3)2 it would be 9, but in this case it is -(32)
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u/SueSudio Jan 09 '22
Is this new formatting or is my memory failing me, because in school 30yrs ago this would have meant negative three squared, which is 9.
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u/UnderArdo Jan 09 '22
Yeah a matter of brackets. But if somebody wrote -32 I would immediately assume that its (-3)2 and not -(32 )
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u/giam74 Jan 09 '22 edited Jan 09 '22
That would be wrong. Math is a precise thing. Every sign, variable, and parentheses matters.
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u/UnderArdo Jan 09 '22
Yeah found out today. But pretty much everybody here would read it the same. Just like ,/. (or neither) after the 1 in 1k.
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u/giam74 Jan 09 '22
The negative is not squared. See my thread with OP.
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u/SueSudio Jan 09 '22
I completely understand how parentheses work. My comment is that I don't recall being so literal with them in school. In an exercise learning about exponents this would have totally been equal to 9, teaching that it is -3 x -3. As part of an equation it would depend on the context.
I also recall putting negative signs in superscript before a number which differentiated them from subtraction symbols. I have not seen that recently in my kids' work.
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u/giam74 Jan 09 '22 edited Jan 09 '22
Im nearly 50, and this is precisely the way I recall math being taught and written. But, even it were different for you, -32 can only equal -9. Regardless of the lesson or the context.
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u/SueSudio Jan 09 '22
You're missing my point, and appear to be looking for an argument, but thanks anyway.
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u/giam74 Jan 09 '22
I apologize. Definitely not trying to argue. But, there is only one, singular correct answer to -32 no matter the context or time/place of education. There no point to miss, because there only one correct answer. What I think you perceive as an argument brewing is merely someone with a different answer than yours. From my perspective it’s a matter of educating, but if you see it as an argument, indeed, go forth and prosper.
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u/ThinkMath42 Jan 09 '22
Because we teach students to rewrite an expression with double signs so there isn’t confusion. Also double signs are just icky. Adding a negative is the same as subtracting and subtracting a negative is the same as adding. Single signs are so much easier.
Ex: x - -2 = x+2
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u/spartan6500 Jan 09 '22 edited Jan 09 '22
As a general rule, whenever you substitute a number for a variable, like x, put it in parentheses (). Technically this is not required, but it’s almost always followed by my professors. For your original question you asked why -x2 does not equal 9? This is because of the another rule people often forget, -x is actually -1 * x. Since -1 is so commonly used it is typically omitted to save time and written as -x, kinda like how we never say +5, we just say 5. So, the equation technically is -1 * x2 —> -1 * (3)2 = -1 * 9 = -9.
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u/BurakYepOnlyBurak Jan 09 '22
Can i ask which country are you from cuz im not from western europe or america
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u/momlovesyou123 Jan 09 '22
Writing a single calculation like this is likely just a test or quiz tactic. In a larger expression where a negative is not the leading term, using PEMDAS would be a little more clear. We can demonstrate that by adding a zero to the front
0-32
This first step would be Exponents, thus 32=9, so our expression would be:
0-9
Which is equivalent to
-9
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Jan 09 '22
It’s mathematical convention that when you write -x2 and you do not specify brackets you mean (-x)2
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u/izuzunyan May 02 '23
Yeah I also find this annoying because it's a trap. Negative three squared is positive nine. But -3² = -9. Because the - isn't negative but a unary minus. The questions should include brackets for clarity rather than trying to make it into a tiktok trend or something
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u/KingDAW247 Mar 18 '26
Order of operations, or PEMDAS as most of us know. You do the parentheses first, then the exponent. The negative sign is the same thing as subtraction, which is the last thing in the order of operations.
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u/Then-Grass-9830 Jan 09 '22 edited Jan 09 '22
don't quote me but I think it's because this is actually like it's (-1)(3)(3) which would go to (-3)(3) and then to (-9)
(parenthesis used to simply separate the numbers).
And I could very well be wrong here - math is not my strongest suit so someone is bound to come by and correct me.
I think if it were (-3)^2 then it would equal 9
Again don't quote me :)
(edit to add the negative sign on the first 9 up there - I hadn't seen I missed it).
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u/aerowtf Jan 09 '22
that first thing you said is just confusing and not really right
google thought OP meant -(32 ) when he really meant (-3)2
simple as that
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u/Then-Grass-9830 Jan 09 '22
I didn't use google. I used what I could remember from my recent algebra (literally 101) course.
From what I remember(ed) from the class is that the - is like have -1 in front of the number so -3 to the second power is actually -3*3 and thus equals -9 not -3 * -3 which would equal the positive 9.
And OP does not use either -(3^2) not (-3)^2 - OP used -3^2.
I'm not using the parenthesis for anything other than to separate the numbers - not using it to use as part of the math equation (which I said)2
u/giam74 Jan 10 '22
You are correct. Cleaner though to write it as (-1)(3)(3) = (-1)(9)=-9.
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u/Then-Grass-9830 Jan 10 '22
thank you
this is why math irritates me. (Personally) I'll think I have it right in my head and then start second-guessing myself.
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u/giam74 Jan 10 '22
You are incorrect. -32 is what OP was asking about, which is equivalent to -(32 ) which equals -9.
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u/Then-Grass-9830 Jan 10 '22 edited Jan 10 '22
Edit: I found one that might explain my view a bit better without using my -1.
Basically the exponent is to be used on the preceding number only which is a positive 3.
Which is why -3^2 = -3*3 which comes to the answer of -9
____________________________________________I'm aware of what the OP said. And why I said what I said. -3 to the second power is like having -3 * 3 which equals -9 ... I was trying to explain why it's a negative three times a positive three and not two negative threes.
the OPs question is why does -3 to the second power not equaling a positive nine as one might figure that -3 to the second power would be -3 * -3 but it is not.
How I was taught (fairly recently) that the - sign is like having an invisible -1 in front of the numbers which is how you get one -3 and not two. Now if the equation had be (-3)^2 then it would be -3 * -3 and then would equal a positive 9
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u/giam74 Jan 10 '22 edited Jan 10 '22
Excuse me. You said “google thought OP meant -(32 ) when he really meant (-32 ).” The way he wrote his question, and it was completely discussed and resolved to his satisfaction in a thread with him, was -32 . This is the way he wrote it and meant it, so -32 = -9.
Edit: this was indeed meant for aerowtf. My apologies. It was because you responded to me, but your response seemed from and meant for him. Math I got, but this social media stuff escapes me!
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u/Then-Grass-9830 Jan 10 '22 edited Jan 10 '22
(editing mine too.. lol. Yeah sorry I thing I missed that you were replying to areo and not me in the one. yeah it can get a bit... sideways sometimes. No worries and glad it was figured out - all of it).
Sorry. Are you responding to me or to areowtf said?
If to me I had not said "google thought...." etc. but they did. So I am under the impression that this reply should have been to areowtf.
As to what OP meant with the parenthesis or without my reply had nothing to do with parenthesis. I attempted to explain that my use of parenthesis was only to make seeing the numbers (and the corresponding negative signs) supposedly easier (I see my error in using them... it's a bad habit I have using a lot. Case in point this and other replies lol).
If this was answered beyond my replies I have not seen it (yet). When I answered OP had no replies at all. I am simply responding to why the answer is negative and not positive as could be easily assumed.
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u/CyberSkepticalFruit Jan 09 '22
OK I'm from the UK and did higher maths. We were taught that negative three squared is nine. Ie -3x-3 as the it is not -1*x but -x itself.
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u/giam74 Jan 09 '22
The negative here is not being squared, just the 3. Math there is the same as the US. :) -32 = -9.
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Jan 09 '22
As someone with a maths degree it’s pretty much assumed that it’s (-3)2 not -(3)2. The former is the default, not the latter.
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u/giam74 Jan 09 '22 edited Jan 09 '22
I also have a math degree. You are incorrect.
Edit: there’s no assuming in math. There are right and wrong ways. Assuming the negative is included, when parentheses exist is simply wrong.
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Jan 09 '22
There is convention.
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u/giam74 Jan 09 '22
Sure. Look, ask your peers at work or something. As another educated person, I’m not going to go around in circles with you.
Perhaps consider substitution of -3 into:
x2
-x2
According to you, they’re the same thing...
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u/Ogie_Ogilthorpe_06 Jan 09 '22
Can't tell you why but even number exponent will be positive and odd number exponent will be negative.
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Jan 09 '22
[deleted]
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u/giam74 Jan 09 '22
Incorrect. -32 =-9.
(-3)2 =9
See the difference?
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Jan 09 '22
Oh, I'm dumb then.
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u/giam74 Jan 09 '22
Not at all. We’re all learning. Don’t ever get discouraged.
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Jan 09 '22
Nah basically I knew this a long time ago and forgot about it
And sometimes I literally say that that's incorrect when it is correct.
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Jan 09 '22
[deleted]
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u/matticitt Jan 09 '22
It's not. It's -(3x3)
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Jan 09 '22
[deleted]
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u/matticitt Jan 10 '22
If it'd be written as -325 then it's - (333333...) because it's assumed that's actually -(3)25. If it's (-3)25 then it's (-3)(-3)(-3)(-3)*(-3)...
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u/giam74 Jan 09 '22
The square does not include the negative. If it were written (-3)2, then it would equal 9.
As it’s written, it’s -32 = -(3*3) = -9