
Factoring problem.
Hello, I am reviewing some algebra concepts for a class I will be taking in the spring. I a trying to factor the polynomial: x^{4}11x^{2}y^{2}+y^{4}. I know the answer is (x^{2}3xyy^{2})(x^{2}+3xyy^{2}). A hint was given to add a term to make a complete square, and then immediately subtract the term which yields a difference of two squares which can then be factored. I cannot figure out what term to add to this equation to put it in the form of a difference of two squares. If someone could explain to me the steps to take in order to factor this, or provide some intuition on how this works I would greatly appreciate it. Thank you for your time and consideration.

Re: Factoring problem.
You could write:
$\displaystyle x^411x^2y^2+y^4=(x^42x^2y^2+y^4)9x^2y^2=(x^2y^2)^2(3xy)^2=$
$\displaystyle (x^2y^2+3xy)(x^2y^23xy)=(x^2+3xyy^2)(x^23xyy^2)$

Re: Factoring problem.
Thank you for your help, I don't know why I didn't see that before.