Even if the x-x term didn’t exist, the equation is already simplified (fully factored) so there is nothing to do anyway.
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.
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 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.
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
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.
0 BCE kind of sucked. Thankfully, they figured it out and 0 CE was awesome.
TIL they had ghost concerts back then
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 mehMathematicians do weird stuff to get more letters, but I’ve never seen anyone use x and 𝑥 for different things
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…
0
Now I want pie.
