A two variable Inequality Show that $(a^2+b^2)(a^4+b^4) \geq (a^3+b^3)^2$ 
Can we go like this : $(a^2+b^2)=(a+b)^2-2ab \& (a^4+b^4) = (a^2+b^2)^2-2a^2b^2$  and right hand side of the inequality : $[(a+b)^3-3ab(a+b)]^2$

$(a^2+b^2)(a^4+b^4)-(a^3+b^3)^2$
$=(a^6+a^4b^2+a^2b^4+b^6)-(a^6+2a^3b^3+b^6)$
$=a^4b^2+a^2b^4-2a^3b^3$
$=a^2b^2(a^2+b^2-2ab)$
$=a^2b^2(a-b)^2$
$\geq 0$
$∴(a^2+b^2)(a^4+b^4)\geq(a^3+b^3)^2$
Q.E.D.
