You could write:
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}-3xy-y^{2})(x^{2}+3xy-y^{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.