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., ax¹¹+bx¹⁰…+jx²+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)?