Zero
Even if the x-x term didn’t exist, the equation is already simplified (fully factored) so there is nothing to do anyway.
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.
(a)(b) basically means a*b
Ok, wtf. Why write it like this then?
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+1TIL this notation makes it math the text up
(a) (b) = a * b (a+1)(b+1) =/= a+1*b+1Edit: hmm, already shows in a code block so adding backticks didn’t do anything
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.
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
Oops, I should have previewed it, thanks for pointing it out.
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.
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!
Couldn’t you combine a lot of like terms as you went along, though? A polynomial of the order x26 would only have 27 terms.
No, because each coefficient is its own variable; they’re not constants.
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.
For those that struggled like me…
Going from a-z, write out the last three multiplicands.
X-X
Ah
This was impossible to answer prior to 3 BC.
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
Why?
0 wasn’t invented yet.
Mesopotamians invented it because year 0 was approaching, so there was a dire need to represent such number.
TIL they had ghost concerts back then
0 BCE kind of sucked. Thankfully, they figured it out and 0 CE was awesome.
That’s when the number 0 was introduced in India.
Ah, I forgot zero was so recent.
Solution?
0
There’s an (x - x) in there
Technically there is a (x - 𝑥) in there.
U+1D465 != xso this post is a little mehthe first variables aren’t roman. they’re italicized as well. idk where you’re getting the x vs x thing.
Mathematicians do weird stuff to get more letters, but I’ve never seen anyone use x and 𝑥 for different things
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…
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.
duh…
Assuming both x represent the same number. There’s no reason to assume the ellipses should include x-x. Why would alphabetic order be involved at all?
have you never taken math? I’m seriously asking because you’re incredibly wrong in both statements.
Why would alphabetic order be involved at all?
Because the
notation effectively means: fill in the blanks. See https://en.wikipedia.org/wiki/Ellipsis#In_mathematical_notation (or https://en.wikipedia.org/wiki/Iterated_binary_operation if you want more…)Yes for numbers, which these are not.
So your argument is that in the list “a, b, c, …, z” the “…” Bit could be anything and we have no way of knowing what’s there and therefore the problem is unsolvable? Or what are you saying exactly?
Yes. The variables a, b, c, and z must have a stated correlation. Variable names do not implicitly have any relation between them. Ellipses work for numbers because a series of 1, 2, 3 … 100 can be inferred using the rules of mathematics. A series of a, b, c … z cannot; the series can only be inferred using the rules of the English language.
so is the word “simplify”. I guess we’ll never know what they mean by that because if you pretend you don’t speak English, then there’s no way of knowing!
Right. Well, yeah, I guess your pedantic response is a lot more logical than the intended answer that other people have pointed out. Have a nice day!
0
Now I want pie.
