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Answer provided by our tutors
p(p)-4pq+4q(q)-r(r)+4sr-4s(s) =
= p^2 - 4pg + 4q^2 - r^2 + 4sr - 4s^2 =
= (p^2 - 2*2pq + (2q)^2) - (r^2 - 2r*(2s) + (2s)^2) =
= (p - 2q)^2 - (r - 2s)^2 =
= (p - 2q - (r - 2s))(p - 2q + (r - 2s) =
= (p - 2q + 2s - r)(p - 2q - 2s + r) =
= (2s - r - 2q + p)(-2s + r - 2q + p) =
= (2s - r - 2q + p)(-1)(2s - r + 2q - p) =
= - (2s - r - 2q + p)(2s - r + 2q - p)