Show that $(a^2-b^2)(a^4-b^4) \leq (a^3-b^3)^2$ and $(a^2+b^2)(a^4+b^4)\geq(a^3+b^3)^2$ for all $a,b$.
I'm basically new to inequality. I'm starting my first inequality book which is Introduction to Inequality
So this is the first question I stuck on. Hope someone could provide some hints for it. Thanks in advance.