If f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞xn and g(x)=∑n=0∞(−1)nxng(x) = \sum_{n=0}^{\infty} (-1)^n x^ng(x)=∑n=0∞(−1)nxn, what is the coefficient of x2x^2x2 in the Cauchy product f(x)⋅g(x)f(x) \cdot g(x)f(x)⋅g(x)?
000
111
−1-1−1
222