### The Volokh Conspiracy

Mostly law professors | Sometimes contrarian | Often libertarian | Always independent

# Math Puzzle

The formula

(*x*-5)(*x*-4)(*x*-3)(*x*-2)(*x*-1)*x*(*x*+1)(*x*+2)(*x*+3)(*x*+4)(*x*+5)

could of course be expanded out into a polynomial. As you might gather, it would be a polynomial of order 11, with 12 coefficients, i.e., *ax*^{11}+*bx*^{10}…+*jx*^{2}+*kx*+*l*. So far, nothing mysterious here.

What is the value of the sum of all the coefficients, *a*+*b*+…+*j*+*k*+*l*? Show all work!

UPDATE: Relatedly, what is the value of *a*–*b*+…-*j*+*k*–*l* (with the +s and -s alternating)?

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