Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials of smaller degree with integer coefficients.
Hint... input $\displaystyle x^8 + 98x^4 + 1$ at Wolfram|Alpha: Computational Knowledge Engine ... see below
You know from symmetry the LHS has to factor as
$\displaystyle (x^4 + ax^3y + bx^2y^2 + cxy^3 + y^4)(x^4 + dx^3y + ex^2y^2 + fxy^3 + y^4)$
Multiplying this out and matching coefficients in the original will give you the factored equation's coefficients. (It took me two pages, but I got there in the end.)
-Dan
You have probably noticed that the expression to be factored has no $\displaystyle x^7y$ term. This leads to the conclusion that (using the above factorization proposed by topsquark) a = -d. Similarly, we find that c = -f. This should simplify things, if only slightly.