Factorization factor ax (Square-1 of Y) - ay (Square-1 of x)

Factorization factor ax (Square-1 of Y) - ay (Square-1 of x)

ax(y^2-1)-ay(x^2-1)
=axy^2-ax^2y-ax+ay
=axy(y-x)+a(y-x)
=a(y-x)(xy+1)