(a^4+b^4)(a^2+b^2)-(a^3+b^3)^2
=a^6+a^2b^4+a^4b^2+b^6-a^6-2a^3b^3-b^6
=a^2b^4+a^4b^2-2a^3b^3
=(a^2b^2)(a^2-2ab+b^2)
=(a^2b^2)(a-b)^2>0
(a^4b^4)(a^2b^2)>(a^3b^3)^2