this post was submitted on 23 Nov 2024

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Math Memes

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Simplify (sh.itjust.works)

submitted 2 months ago by sjmarf to c/[email protected]

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[–] [email protected] 171 points 2 months ago (1 children)

For those of you who were confused even after reading the comments: (a)(b) basically means a*b. My mind just didn't connect that to the fact that (x-x)=0. in the (a-x)(b-x) stuff is also (x-x) which = 0, and anything * 0 = 0, so no matter the value of literally everything else in the equation, it all equals out to 0 because every single () will get multiplied by (x-x), which is 0. There, hopefully that will clear it up for anyone remaining lost. And like all good jokes, they are always best when you have to explain them.

[–] [email protected] 2 points 2 months ago (3 children)

(a)(b) basically means a*b

Ok, wtf. Why write it like this then?

[–] [email protected] 27 points 2 months ago (1 children)

To make sure what's inside the brackets is resolved internally before they're multiplied with each other.

 (a)  (b)   =   a * b  
(a+1)(b+1) =/= a+1*b+1

[–] brbposting 1 points 2 months ago* (last edited 2 months ago)

TIL this notation makes it math the text up

(a)  (b)   =   a * b  
    (a+1)(b+1) =/= a+1*b+1

Edit: hmm, already shows in a code block so adding backticks didn’t do anything

[–] [email protected] 7 points 2 months ago* (last edited 2 months ago) (2 children)

To expand on what superkret said, in math there is the concept of "order of operations". That is to say, every function in math (add, multiply, divide) has to be done in a specific order. Since multiplication comes before addition and subtraction, if you have a formula like a-x*b-x, you will do x*b first, then a minus the result of x*b, which would give a very different result than if you did a-x and multiplied that by b-x. This is where the parenthesis come in. You are basically saying, resolve every section in parenthesis first using the proper order, then resolve the rest.

My original example (a)(b) was over simplified, because there is no conflict there. You can also do things like (a*x)-(b*x). If there is no operator though, it is assumed multiplication, and I'm unsure why that is.

[–] starman2112 4 points 2 months ago* (last edited 2 months ago) (1 children)

Putting multiple asterisks in a comment makes it look italicized, at least on some Lemmy clients. If you want to have asterisks with *unitalicized* text, you gotta put a \ behind the * to negate the change

[–] [email protected] 3 points 2 months ago

Oops, I should have previewed it, thanks for pointing it out.

[–] [email protected] 1 points 2 months ago

(a)(b) basically means a*b.

Actually it's (axb), since a(b+c)=(ab+ac). This is where a lot of people go wrong in the order of operations questions you see on socials - removing the brackets too soon. 1/ab=1/(axb) NOT 1/axb. If a=2 and b=3 then 1/ab=1/(2x3)=1/6, but 1/axb=1/2x3=3/2. Note that this also means it gets solved in the Brackets step of order of operations, NOT the "Multiplication" step (another common mistake).

If there is no operator though, it is assumed multiplication

It's not "multiplication", it's a Product, a single number written as a product of factors. If a=2 and b=3 then ab is 6 written as the product of 2 and 3. ab=(2)(3)=(2x3)=6. axb=ab, 2x3=6, axb=2x3, ab=6.

"I’m unsure why that is."

To show it's a single number, not 2 separate numbers to be multiplied. Think of things like F=ma. You have to show that ma is a single number (equal to the Force), not 2 separate numbers multiplied., mxa. If you were doing something like dividing by the Force, then you have to have 1/ma=1/(mxa), NOT 1/mxa.

[–] Jyek 3 points 2 months ago (1 children)

Because you wrote a lot less when writing it this way. Groups of terms beside each other are multiplying each other and you have to solve what's inside of those groups before multiplying them together.

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[–] [email protected] 89 points 2 months ago (2 children)

For those that struggled like me…

Going from a-z, write out the last three multiplicands.

[–] [email protected] 54 points 2 months ago (1 children)

X-X

[–] [email protected] 2 points 2 months ago (1 children)

For those of you who still struggled like me, a multiplicand in this case refers to one of the (n-x) terms.

[–] [email protected] 3 points 2 months ago

a multiplicand in this case refers to one of the (n-x) terms

Well, that's what was apparently meant, but in fact the correct terminology here is factors. There's only multiplicands (and multipliers) with an explicit multiplication sign. axb - multiplicand a and multiplier b, ab - Term with factors a and b, and a is the coefficient of this Term.

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[–] [email protected] 53 points 2 months ago (24 children)

Even if the x-x term didn't exist, the equation is already simplified (fully factored) so there is nothing to do anyway.

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[–] [email protected] 47 points 2 months ago (2 children)

Fun fact, omitting the (x-x) zero term and expanding the entire polynomial, you'd get something with 2^25 = 33,554,432 terms. May be slightly excessive!

[–] threelonmusketeers 8 points 2 months ago (1 children)

Couldn't you combine a lot of like terms as you went along, though? A polynomial of the order x^26^ would only have 27 terms.

[–] [email protected] 2 points 2 months ago (2 children)

No, because each coefficient is its own variable; they're not constants.

[–] [email protected] 1 points 2 months ago

because each coefficient

There's only 1 coefficient - in this case it's (a-x) - the rest are just factors.

they’re not constants

They could be - we haven't been given that information.

[–] threelonmusketeers 1 points 2 months ago* (last edited 2 months ago)

Huh, I'm so used to polynomials being in the form ax^2 + bx + c that I never considered that every letter might be a variable.

[–] [email protected] 2 points 2 months ago

33,554,432 terms

Actually it would be that many factors. The whole thing is a single Term.

[–] [email protected] 41 points 2 months ago (2 children)

This was impossible to answer prior to 3 BC.

[–] [email protected] 16 points 2 months ago

Unless you were Mayan. They had a concept of zero, or so I heard. But they lacked the letters, a-z and the parentheses :p

[–] threelonmusketeers 2 points 2 months ago (2 children)

Why?

[–] [email protected] 36 points 2 months ago (2 children)

0 wasn’t invented yet.

Mesopotamians invented it because year 0 was approaching, so there was a dire need to represent such number.

[–] [email protected] 2 points 2 months ago

TIL they had ghost concerts back then

[–] [email protected] 1 points 2 months ago* (last edited 2 months ago)

0 BCE kind of sucked. Thankfully, they figured it out and 0 CE was awesome.

[–] [email protected] 6 points 2 months ago (1 children)

That’s when the number 0 was introduced in India.

[–] threelonmusketeers 4 points 2 months ago

Ah, I forgot zero was so recent.

[–] [email protected] 13 points 2 months ago (1 children)

Solution?

[–] [email protected] 64 points 2 months ago (12 children)

There’s an (x - x) in there

[–] [email protected] 10 points 2 months ago* (last edited 2 months ago) (2 children)

Technically there is a (x - 𝑥) in there. U+1D465 != x so this post is a little meh

[–] [email protected] 11 points 2 months ago (2 children)

Mathematicians do weird stuff to get more letters, but I've never seen anyone use x and 𝑥 for different things

[–] threelonmusketeers 5 points 2 months ago

I've never seen anyone use x and 𝑥 for different things

Yeah, me neither. I have had situations where I needed to distinguish between u, v, nu, and upsilon though. I had to be very careful with my handwriting that day...

[–] [email protected] 4 points 2 months ago

They also wouldn't want to be ambiguous. If I was trying to write this problem the a, b, c... would get replaced by something like a_1, a_2,..., a_26 to be clearer. This problem works as a fun gotcha but isn't something that would come up in the real world.

[–] [email protected] 1 points 2 months ago

the first variables aren't roman. they're italicized as well. idk where you're getting the x vs x thing.

[–] [email protected] 6 points 2 months ago (1 children)

duh...

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[–] [email protected] 5 points 2 months ago

[–] [email protected] 2 points 2 months ago

Now I want pie.

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