Simplify the expression

x²⁶ - x²⁵(a+b+c+...+z) + x²⁴(ab+ac+...+az+bc+...+bz+...+yz) - x²³(abc+...+abz+acd+...+acz+...+xyz) + ... + abc...z

(In reply to A Guess by tomarken)

I looked around and I am willing to bet that the expression given in the problem can be factorised in terms of Vieta's formula for  Polynomial roots ( ref: http://mathworld.wolfram.com/VietasFormulas.html)

This would provide another likely  avenue to deduce or verify  the final answer  to this problem.

Edited on June 16, 2006, 10:14 am

Edited on June 16, 2006, 10:16 am

Edited on June 16, 2006, 10:22 am

Posted by K Sengupta on 2006-06-16 10:14:24