book shows answer as x^4+4x^2y^2+4y^4-4x^2y^2=(x^2+2y^2)^2-(2xy)^2=(x^2+2y^2-2xy)(x^2+2y^2+2xy) What is happening here and what steps am i missing???
What they have done is add and subtract which, of course, doesn't change the actual value. But that does change the form so that it we can think of it as which is a "difference" of two squares. You probably know that so that last is .