Distribute terms in parentheses, and then regroup terms in the form of the difference of squares

(m^2-1)(n^2-1)+4mn

=m^2n^2-m^2-n^2+1+4mn

=m^2n^2+2mn+1-(m^2-2mn+n^2)

=(mn+1)^2-(m-n)^2

=(mn-m+n+1)(mn+m-n+1)