(p⁴+q⁴)²-4p⁴q⁴
=(p⁴+q⁴)²-(2p²q²)²
=(p⁴+q⁴+2p²q²)(p⁴+q⁴-2p²q²)
=(p²+q²)²(p²-q²)²
=(p²+q²)²(p-q)²(p+q)²