Explanation
In this factorization formula used:
(a + b)2 = (a2 + 2.a.b + b2) & (a – b)2 = (a2 – 2.a.b + b2)
(p2 – q2) (x2 – s2) + 4pqxs
\rightarrow\ {p2(x2 – s2) – q2(x2 – s2)} + 2pqxs + 2pqxs
\rightarrow\ (p2x2 – p2s2 – q2x2 + q2s2) + 2pqxs + 2pqxs
\rightarrow\ P2x2 + 2pqxs + q2s2 – p2s2 + 2pqxs – q2x2 [rearrange]
\rightarrow\ (p2x2 + 2pqxs + q2s2) – (p2s2 – 2pqxs + q2x2)
\rightarrow\ {(px)2 + 2pqxs + (qs)2} – {(ps)2 – 2pqxs + (qx)2}
\rightarrow (px + qs)2 – (ps – qx)2
\rightarrow\ {(px + qs) + (ps – qx)} {(px + qs) – (ps – qx)}
Ans: (px + qs + ps – qx) (px + qs – ps + qx)