How do we show that $x^5y^3 + x^4y^4 + x^3y^5$ is $\Omega(x^3y^3)$ Basically I'm wondering how I can show that $x^5y^3 + x^4y^4 + x^3y^5$ is $\Omega(x^3y^3)$.  Any ideas?  Thanks a lot!

Denote the expression in the OP $F(x,y)$. For any $x,y >0 \ F(x,y) \geq 3 x^3 y^3 = \Omega (x^3 y^3)$
EDIT: $F(x,y) \geq x^3y^3 + x^3 y^3 + x^3 y^3 = 3 x^3 y^3 = \Omega(x^3 y^3)$ since $x^5>x^4>x^3$. Same with $y$.
