I'm working on some equations in number theory and I stuck on below inequality : 

$$p^{\alpha +1}q^{\beta +1}-2p^{\alpha+1}q^{\beta}-2p^{\alpha}q^{\beta +1}+2p^{\alpha}q^{\beta}+p^{\alpha+1}+q^{\beta+1}-1 > 0$$

Here $p$ and $q$ are distinct prime numbers and $p,q >2$ and $\alpha\,,\beta$ are positive integer numbers.

Can somebody help me to prove that or find counterexample , although I believe that the inequality is true.