The number of distinct ordered pairs $(x,y)$ where $x$ and $y$ have positive integral values satisfying the equation $x^4y^4-10x^2y^2+9=0$ is:
$\text{(A) } 0\quad \text{(B) } 3\quad \text{(C) } 4\quad \text{(D) } 12\quad \text{(E) } \infty$
Let $(xy)^2=a$. The expression given is equal to $a^2-10a+9=0$, which can be factored as $(a-9)(a-1)=0$. Thus, we have $a=(xy)^2=9$ and $a=(xy)^2=1$. Because $x$ and $y$ are positive, we can eliminate the possibilities where $xy$ is negative. From here it is easy to see that the only integral pairs of $x$ and $y$ are $(3, 1), (1, 3)$, and $(1, 1)$. The answer is $\fbox{B}$.