text: # Question regarding what appears to be an identity
  
  This is an MCQ we were posed in school recently (I hope you don't mind elementary stuff):
  
  What is $(x-a)(x-b)(x-c)...(x-z)$ ? Options:
  
  $0$
  
  $1$
  
  $2$
  
  $(x^n)-(abcdef...z)$
  
  -
  Are you sure it didn't go up to $x-z$? – mixedmath Sep 27 '12 at 2:56
  @mixedmath Surely it did, or else none of the choices is correct (not that I particularly like the "solution" in that case). – Austin Mohr Sep 27 '12 at 2:58
  Oh yes, it did. I'm so sorry. But the last option was still $x^n - (abc...z)$ AFAIK. I lost the test paper :( – Soham Chowdhury Sep 27 '12 at 2:59
  How does it matter if it's $n$ or $z$? – Soham Chowdhury Sep 27 '12 at 3:01
  @SohamChowdhury The fact that $n$ or $z$ actually makes a difference is something you should think about. – Erick Wong Sep 27 '12 at 3:07
  
  There is a very basic trick to this problem. It all comes down to a single term (if that's the proper word for it...).
  
  The only real hint I can give is $x$ is a letter between $a$ and $z$...
  
  -
  +1, Very cool! Also, Thank you @DonAntonio for pointing where I went wrong. – NoChance Sep 27 '12 at 4:11
  Ah, I see... $(x-a)(x-b)..(x-x)..(x-z)$ where $(x-x)$ is 0. Nice! – Soham Chowdhury Sep 27 '12 at 4:22
  
  Hint $\$ What is $\rm\ (24-1)(24-2)(24-3)\cdots (24-26)\$ ?
  
  And what is $\rm\,(x_{24}\!-x_1)(x_{24}\!-x_2)(x_{24}\!-x_3)\cdots (x_{24}\!-x_{26})\$ ?
  
  -
  @Thanks for the hint. Very good point. – NoChance Sep 27 '12 at 4:08
explanation: The document contains a math question presented as a multiple-choice question (MCQ) and a discussion about the correct answer. The question asks for the value of the expression \((x-a)(x-b)(x-c)...(x-z)\) with given options. The discussion includes hints and a realization that the term \((x-x)\) makes the entire product zero.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Question regarding what appears to be an identity
  
  This is an MCQ we were posed in school recently (I hope you don't mind elementary stuff):
  
  What is $(x-a)(x-b)(x-c)...(x-z)$ ? Options:
  
  $0$
  
  $1$
  
  $2$
  
  $(x^n)-(abcdef...z)$
  
  -
  Are you sure it didn't go up to $x-z$? – mixedmath Sep 27 '12 at 2:56
  @mixedmath Surely it did, or else none of the choices is correct (not that I particularly like the "solution" in that case). – Austin Mohr Sep 27 '12 at 2:58
  Oh yes, it did. I'm so sorry. But the last option was still $x^n - (abc...z)$ AFAIK. I lost the test paper :( – Soham Chowdhury Sep 27 '12 at 2:59
  How does it matter if it's $n$ or $z$? – Soham Chowdhury Sep 27 '12 at 3:01
  @SohamChowdhury The fact that $n$ or $z$ actually makes a difference is something you should think about. – Erick Wong Sep 27 '12 at 3:07
  
  There is a very basic trick to this problem. It all comes down to a single term (if that's the proper word for it...).
  
  The only real hint I can give is $x$ is a letter between $a$ and $z$...
  
  -
  +1, Very cool! Also, Thank you @DonAntonio for pointing where I went wrong. – NoChance Sep 27 '12 at 4:11
  Ah, I see... $(x-a)(x-b)..(x-x)..(x-z)$ where $(x-x)$ is 0. Nice! – Soham Chowdhury Sep 27 '12 at 4:22
  
  Hint $\$ What is $\rm\ (24-1)(24-2)(24-3)\cdots (24-26)\$ ?
  
  And what is $\rm\,(x_{24}\!-x_1)(x_{24}\!-x_2)(x_{24}\!-x_3)\cdots (x_{24}\!-x_{26})\$ ?
  
  -
  @Thanks for the hint. Very good point. – NoChance Sep 27 '12 at 4:08
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question presented as a multiple-choice question (MCQ) and a discussion about the correct answer. The question asks for the value of the expression \((x-a)(x-b)(x-c)...(x-z)\) with given options. The discussion includes hints and a realization that the term \((x-x)\) makes the entire product zero.
  
  Label: question-and-answer