# Factoring problem.

• Nov 23rd 2012, 10:07 AM
KhanDisciple
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.
• Nov 23rd 2012, 10:14 AM
MarkFL
Re: Factoring problem.
You could write:

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

\$\displaystyle (x^2-y^2+3xy)(x^2-y^2-3xy)=(x^2+3xy-y^2)(x^2-3xy-y^2)\$
• Nov 23rd 2012, 01:40 PM
KhanDisciple
Re: Factoring problem.
Thank you for your help, I don't know why I didn't see that before.