Multiply the series (∑n=1∞xn)(∑n=0∞(−1)nxn)\left(\sum_{n=1}^{\infty} x^n\right)\left(\sum_{n=0}^{\infty} (-1)^n x^n\right)(∑n=1∞xn)(∑n=0∞(−1)nxn) using the Cauchy product and find the coefficient of x2x^2x2.
111
000
−1-1−1
222