We have, (1+x−2x2)6=1+a1x+a2x2+...+a12x12 Put x=1 on both sides we. get 0=1+a1+a2+a3+a4+...+a12...(i) Put x=−1 on both sides, we get 64=1−a1+a2−a3+a4−a5...+a12....(ii) Adding Eqs. (i) and (ii). we get 64=2+2(a2+a4+a6+...a12) ⇒a2+a4+a6...+a12=31