<s>[INST] Factoring $x^4-11x^2y^2+y^4$ I am brushing up on my precalculus and was wondering how to factor the expression
$$
x^4-11x^2y^2+y^4
$$
Thanks for any help!
 [/INST] $$
\begin{align}
x^4-11x^2y^2+y^4
&=\left(x^2-y^2\right)^2-(3xy)^2\\
&=\left(x^2-3xy-y^2\right)\left(x^2+3xy-y^2\right)\\
&=\left(x-\tfrac{3-\sqrt{13}}2y\right)\left(x-\tfrac{3+\sqrt{13}}2y\right)\left(x+\tfrac{3-\sqrt{13}}2y\right)\left(x+\tfrac{3+\sqrt{13}}2y\right)
\end{align}
$$
</s>