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.
this post was submitted on 23 Nov 2024
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For those that struggled like me…
Going from a-z, write out the last three multiplicands.
X-X
Ah
For those of you who still struggled like me, a multiplicand in this case refers to one of the (n-x) terms.
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.
Even if the x-x term didn't exist, the equation is already simplified (fully factored) so there is nothing to do anyway.
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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What's the right term then? "Multiplied through?" ? "Complicated?"
Expand
Expand
As in "expand and simplify". If you only expanded then you haven't simplified yet.
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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 x^26^ 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.
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.
33,554,432 terms
Actually it would be that many factors. The whole thing is a single Term.
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 != x so this post is a little meh
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.
the first variables aren't roman. they're italicized as well. idk where you're getting the x vs x thing.
duh...
Do do, do do do do do....
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0
Now I want pie.
Zero
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