Use Newton's identity: if sk=xk+yks_k = x^k + y^ksk=xk+yk and p=x+yp = x + yp=x+y, q=xyq = xyq=xy, then s2=p2−2qs_2 = p^2 - 2qs2=p2−2q. Find s4s_4s4 in terms of ppp and qqq.
p4−4p2q+2q2p^4 - 4p^2q + 2q^2p4−4p2q+2q2
p4−2q2p^4 - 2q^2p4−2q2
p4−4q2p^4 - 4q^2p4−4q2
p4+2q2p^4 + 2q^2p4+2q2