Final answer:
The polynomial (y⁴)² - 2(y⁴) is a difference of squares and factors to (y⁴ + √2)(y⁴ - √2), which is none of the options provided. It's possible there was a typo in the options.
Step-by-step explanation:
The polynomial in question is (y⁴)² - 2(y⁴). To factor this completely, we recognize it as a difference of squares. A difference of squares is a polynomial of the form a² - b² which can be factored into (a + b)(a - b). In this case, a is y⁴ and b is √2 because when squared, it gives 2 ((√2)² = 2). We cannot take the square root of y⁴ because it is already a square in itself. Thus, the completely factored form of the polynomial is (y⁴ + √2)(y⁴ - √2), which is not one of the provided options. Hence, it seems there may have been a typo in the options provided.