This may look complicated at first glance; trust that GMAT problems that appear to involve complex calculations usually do not.

In this case, the trick is recognizing the presence of the difference of squares. Rearrange the first term:

(y^2 + x)(y^2 - x)(x^2 + y^4) =

Those first two terms are of the same form as (x + y)(x - y), which results in (x^2 - y^2). Here, the values of x and y are a little different, but the principle is the same:

(y^2 + x)(y^2 - x) = (y^2)^2 - x^2 = y^4 - x^2

That leaves us with:

(y^4 - x^2)(x^2 + y^4) =

It's still not simple, but that may look familiar. Rearrange the second term, and the difference of squares appears again:

(y^4 - x^2)(y^4 + x^2)
= (y^4)^2 - (x^2)^2
= y^8 - x^4, choice (A).