Question 479507
p - xy
={{{p - (p-n^2)((n+1)^2 - p)}}}
={{{p - (p(n+1)^2 - p^2 - n^2(n+1)^2 + n^2p)}}}
={{{p - p(n+1)^2 + p^2 + n^2(n+1)^2 - n^2p}}}
={{{p - p(n^2 + 2n + 1) + p^2 + n^2(n+1)^2 - n^2p}}}
={{{p - pn^2 - 2pn - p + p^2 + n^2(n+1)^2 - n^2p}}}
={{{- 2pn^2 - 2pn + p^2 + n^2(n+1)^2}}}
={{{- 2pn^2 -n^2  + p^2 - 2pn + n^2 +  n^2(n+1)^2}}}
={{{- 2pn^2 -n^2  +(p-n)^2 +  n^2(n+1)^2}}}
= {{{-n^2(1 + 2p) + (p-n)^2 + n^2(n+1)^2}}}
={{{n^2((n+1)^2 - (1+2p)) + (p-n)^2}}}
= {{{n^2(n^2 + 2n - 2p) + (p-n)^2}}}
= {{{n^4 - 2n^2(p-n) + (p-n)^2}}}
={{{(n^2 - (p-n))^2}}}
={{{(n^2 + n - p)^2}}}
and the proof is complete...