Why a Negative Number Squared is Negative - Wednesday's Why

Those tricky negatives are at it again. In this video we talk about why a negative squared can be a negative...it really has to do with the order of operations.

[dilipgowdan]

Bruh I was studying physics where I came across this problem in a numerical and I had to rethink if I was dreaming coz I got hella confused tho I had been doing math for almost 15 years. Now I got how it is. Thank you :)

[Jesse_Scoccimarra]

What you mentioned of it being -1 • 2^2 really helped me understand it, thanks

[brandonheald]

I might have laughed a little too hard at what you did in the beginning. Some reason it got me good. Great video.

[maynen]

Unless I'm missing an important detail, here comes a deep question...

I understand the rule but I don't understand why this rule would occur like this. It's not about one number minus another where I understand that you should apply the rule. In the example of "-3", this minus is just a part of the number itself. The minus in "-3" is one part of this expression/word "number". The 3 is the other part of the word number. Togheter they create the number "-3".

Further, to square something with 2 means to take a number and multiply it with itself. Now if you don't do that and only take the "3" and multiply with 3 again. That means that -3 is not number itself. It's a value. Which means that any negative amount/value are not numbers. Only positive numbers are numbers.

[EmpyreanLightASMR]

Thank you for teaching me that I don't get this at all. I'm literally in the middle of a quadratic formula and even though I can look up the answer online, I know the truth is, I have no freaking clue what I'm doing. I hate to say it, but I still don't get it.

[mikeoxlong]

I thought I was experiencing Mandela effect on squaring negative numbers.

[talderson]

Is there an explanation of why two negatives multiply to positive? I don't know if I ever knew or it's just been so long I've forgotten.

[Agateophobiadragon]

So, WHY is -2² = -1•2² but apparently (-2)² is equal to -2•-2?

[youraverageguy]

i almost punched my fcking monitor cuz im so frustrated and it's so fcking hot in my appartment when i stumbled on this fcking mind boggling paradox. thank you for enlightening my feeble mind.

[AyushsGoPro]

How do I use it in the quadratic formula

[TheMoFauxs]

So basically it’s a matter of understanding what is being asked. -3^2=-9 because it’s asking for the negative of 3 squared. Not to square negative 3. I think?

[mylightbsunrise]

There was a variable equation involving this that I got wrong today on the test. If only I had watched this video before the test lol

[ivynovinsproducts]

This logic is flawed though. First of all, the term being squared is (-5). IF you squared 5 first, what are you subtracting it from in a standalone situation. The subtraction operation and the negative sign in front of the number 5 are not the same thing

The negative sign at the beginning of -5^2 cannot be a subtraction operation; a problem cannot start with an operation.

That same logic would imply that the problem *5^2 is possible

[BobCrain-mvlh]

So what you're saying is... a negative number is not a number, but actually -1 multiplied by a number?

[mf]

This is wrong. The operator "subtraction" or (-) is different than the "unary minus" or (-) notation for negative numbers. It is meaningless to have a "subtraction" operator at the beginning of a standalone expression. So the (-) in this case must be the "unary minus" notation.

Now, the "unary minus" (-) notation is not an operator. Negative numbers are their own entities which we happen to notate with this (-). So order of operations does not apply as there is only one operator and you cannot order a single operator other than one way.

So the only way to interpret -3^2 is as (-3)^2.

This is a case of people naively following rules and not understanding what numbers are.

[rikkasatrio]

Lol I remember the whole class were fighting over this when I was in middle school

[winniemunthali]

I was doing this in class and I did not understand so if puns this and it really helped thank you

[abbyfitzpatrick]

This was super helpful thank you so much

[ToyaF]

This just confirms why I don't math 😳

[lawrencevautier]

Wait, so if you just saw in a maths textbook what -2 squared is, what would the final answer be?