Question 39795
{{{(x^2+4xy^2+4y^4)-y^2}}}

You have done well.

You now have (x+(2y^2)^2 - y^2

This is the difference of squares: just like a^2-b^2
which factors into (a+b)(a-b)

So, you get 
  (x+2y^2-y)(x+2y^2+y)
Cheers,
Stan H.