# Math Help - Factoring problem.

1. ## 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: x4-11x2y2+y4. I know the answer is (x2-3xy-y2)(x2+3xy-y2). 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.

2. ## Re: Factoring problem.

You could write:

$x^4-11x^2y^2+y^4=(x^4-2x^2y^2+y^4)-9x^2y^2=(x^2-y^2)^2-(3xy)^2=$

$(x^2-y^2+3xy)(x^2-y^2-3xy)=(x^2+3xy-y^2)(x^2-3xy-y^2)$

3. ## Re: Factoring problem.

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