Q.Factorize: (a^2 - 1)(b^2-1) + 4ab?

(a^2-1)(b^2-1)+4ab 

= a^2 b^2 - a^2 - b^2 +1+ 4ab 

Now break 4ab into 2ab+2ab 

= a^2 b^2 - a^2 - b^2 +1+ 2ab+2ab 

Now arrange 

= (a^2 b^2+ 2ab +1) - (a^2 - 2ab+ b^2) 

=(ab +1)^2 - (a-b)^2 

Using Formula x^2 -y^2 = (x-y)(x+y) 

=[(ab+1) + (a-b)] [(ab+1) - (a-b)] 

=(ab+1+a-b)(ab+1-a+b)