Simplify : mathmemes

[–] greybeard@lemmy.one 148 points 10 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.

[–] MonkderVierte@lemmy.ml 2 points 10 months ago (3 children)

(a)(b) basically means a*b

Ok, wtf. Why write it like this then?

[–] superkret@feddit.org 27 points 10 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@sh.itjust.works 2 points 10 months ago* (last edited 10 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

[–] greybeard@lemmy.one 6 points 10 months ago (1 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-xb-x, you will do xb 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 (ax)-(bx). If there is no operator though, it is assumed multiplication, and I'm unsure why that is.

[–] starman2112@sh.itjust.works 3 points 10 months ago* (last edited 10 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

[–] greybeard@lemmy.one 2 points 10 months ago

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

[–] Jyek@sh.itjust.works 2 points 10 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.

[–] SmartmanApps@programming.dev 1 points 10 months ago

Groups of terms beside each other are multiplying each other

Actually the whole thing is a single Term. Terms are separated by operators and joined by grouping symbols, and there's no operators between the successive brackets.

you have to solve what’s inside of those groups before multiplying them together

You don't have to, but it sure makes the working-out a lot easier if you do!

If a=1, b=2, c=3, d=4, then...

(a+b)(c+d)=(ac+ad+bc+bd)

(1+2)(3+4)=(1x3+1x4+2x3+2x4)=(3+4+6+8)=21

whereas...

(1+2)(3+4)=(3)(7)=(3x7)=21 :-)

[–] Saganaki@lemmy.one 80 points 10 months ago (2 children)

For those that struggled like me…

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

[–] dditty@lemm.ee 52 points 10 months ago (1 children)

X-X

Ah

[–] sem@lemmy.blahaj.zone 2 points 10 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.

[–] SmartmanApps@programming.dev 2 points 10 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.

[–] the_tab_key@lemmy.world 44 points 10 months ago (2 children)

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

[–] SmartmanApps@programming.dev 2 points 10 months ago (10 children)

is already simplified (fully factored)

No it isn't, given one of the factors is equal to zero. That's like saying 2/4 is fully simplified when clearly it isn't. Students lose marks in tests for not simplifying their answers. Writing 2/4 as an answer would only get half-marks. Similarly, the only full-marks answer to this question is 0.

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[–] sem@lemmy.blahaj.zone 1 points 10 months ago (1 children)

What's the right term then? "Multiplied through?" ? "Complicated?"

[–] the_tab_key@lemmy.world 2 points 10 months ago (1 children)

Expand

[–] SmartmanApps@programming.dev 1 points 10 months ago (10 children)

Expand

As in "expand and simplify". If you only expanded then you haven't simplified yet.

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[+] LostXOR@fedia.io 40 points 10 months ago* (last edited 1 month ago) (2 children)

[deleted]

[–] threelonmusketeers@sh.itjust.works 6 points 10 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.

[–] SmartmanApps@programming.dev 2 points 10 months ago

33,554,432 terms

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

[–] disguy_ovahea@lemmy.world 35 points 10 months ago (2 children)

This was impossible to answer prior to 3 BC.

[–] anzo@programming.dev 13 points 10 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@sh.itjust.works 1 points 10 months ago (2 children)

Why?

[–] magic_lobster_party@fedia.io 28 points 10 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.

[–] TempermentalAnomaly@lemmy.world 1 points 10 months ago* (last edited 10 months ago)

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

[–] scapegarced@sopuli.xyz 1 points 10 months ago

TIL they had ghost concerts back then

[–] disguy_ovahea@lemmy.world 4 points 10 months ago (1 children)

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

[–] threelonmusketeers@sh.itjust.works 1 points 10 months ago

Ah, I forgot zero was so recent.

[–] atro_city@fedia.io 12 points 10 months ago (1 children)

Solution?

[–] magic_lobster_party@fedia.io 59 points 10 months ago (11 children)

0

There’s an (x - x) in there

[–] copd@lemmy.world 9 points 10 months ago* (last edited 10 months ago) (2 children)

Technically there is a (x - 𝑥) in there. U+1D465 != x.

[–] MBM@lemmings.world 10 points 10 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

[–] joshthewaster@lemmy.world 4 points 10 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.

[–] threelonmusketeers@sh.itjust.works 2 points 10 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...

[–] pyre@lemmy.world 1 points 10 months ago

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

[–] atro_city@fedia.io 5 points 10 months ago (1 children)

duh...

[–] sem@lemmy.blahaj.zone 1 points 10 months ago

Do do, do do do do do....

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[–] sag@lemm.ee 4 points 10 months ago

0

[–] MyTurtleSwimsUpsideDown@fedia.io 2 points 10 months ago

Now I want pie.

[–] iamdefinitelyoverthirteen@lemmy.world 1 points 10 months ago

Zero

Math Memes