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!

$$(x^2 + a y^2) (x^2 + b y^2) = x^4-11x^2y^2+y^4$$
Hence,
$$a + b = -11 \qquad \qquad \qquad a b = 1$$
In SymPy,
>>> a, b = symbols('a b')
>>> solve_poly_system([a + b + 11, a*b - 1], a, b)
             ____             ____               ____             ____  
    11   3*\/ 13     11   3*\/ 13       11   3*\/ 13     11   3*\/ 13   
[(- -- - --------, - -- + --------), (- -- + --------, - -- - --------)]
    2       2        2       2          2       2        2       2      

Thus,
$$\left( x^2 + \left(\frac{-11 - 3 \sqrt{13}}{2}\right) y^2 \right) \left( x^2 + \left(\frac{-11 + 3 \sqrt{13}}{2}\right) y^2 \right) = x^4-11x^2y^2+y^4$$
