For a multilinear polynomial p and a set E of variable indices, the coefficient c_E of the product of variables in E equals the sum of (-1)^(|E|-|U|) p(1_U) over all subsets U of E. The vector 1_U sets precisely the variables in U to one, all others to zero. For E={1,2}, this is p(1,1)-p(1,0)-p(0,1)+p(0,0). For 2+3X+5XY it gives 10-5-2+2=5. Terms missing an index of E cancel in pairs; terms involving an index outside E vanish. If total degree is at most q, coefficients with |E|>q are zero. The empty-set coefficient is p(0).