this post was submitted on 23 Nov 2024

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Simplify (sh.itjust.works)

submitted 4 weeks ago by [email protected] to c/[email protected]

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[–] [email protected] 171 points 4 weeks 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] 3 points 3 weeks ago (3 children)

(a)(b) basically means a*b

Ok, wtf. Why write it like this then?

[–] [email protected] 28 points 3 weeks 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

[–] [email protected] 2 points 3 weeks ago* (last edited 3 weeks 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 3 weeks ago* (last edited 3 weeks 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.

[–] [email protected] 4 points 3 weeks ago* (last edited 3 weeks 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 3 weeks ago

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

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[–] [email protected] 3 points 3 weeks 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] 88 points 4 weeks ago (2 children)

For those that struggled like me…

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

[–] [email protected] 53 points 4 weeks ago (1 children)

X-X

[–] [email protected] 2 points 2 weeks 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 3 points 2 weeks 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.

[–] [email protected] 53 points 3 weeks ago (12 children)

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

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

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

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

Expand

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[–] [email protected] 47 points 3 weeks 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!

[–] [email protected] 8 points 3 weeks 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 3 weeks ago (2 children)

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

[–] [email protected] 1 points 3 weeks ago* (last edited 3 weeks 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.

[–] SmartmanApps 1 points 2 weeks 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.

[–] SmartmanApps 2 points 2 weeks ago

33,554,432 terms

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

[–] [email protected] 41 points 4 weeks ago (2 children)

This was impossible to answer prior to 3 BC.

[–] anzo 16 points 4 weeks 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

[–] [email protected] 2 points 4 weeks ago (2 children)

Why?

[–] [email protected] 36 points 4 weeks 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 3 weeks ago

TIL they had ghost concerts back then

[–] [email protected] 1 points 3 weeks ago* (last edited 3 weeks ago)

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

[–] [email protected] 6 points 4 weeks ago (1 children)

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

[–] [email protected] 4 points 4 weeks ago

Ah, I forgot zero was so recent.

[–] [email protected] 13 points 4 weeks ago (1 children)

Solution?

[–] [email protected] 64 points 4 weeks ago (12 children)

There’s an (x - x) in there

[–] [email protected] 10 points 3 weeks ago* (last edited 3 weeks 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 3 weeks ago (2 children)

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

[–] [email protected] 5 points 3 weeks 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 3 weeks 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 3 weeks 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 4 weeks ago (1 children)

duh...

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

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

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[–] [email protected] 5 points 4 weeks ago

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

Now I want pie.

[–] [email protected] 1 points 3 weeks ago

Zero

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