jmc

We expand the left side to get $(ab{x}^2+(a^2+b^2)x+ab)=26x^2+\square \cdot x+26$. The coefficients of like terms must be equal, so that means $ab=26$. The only possibilities for $(a,b)$ are $(2,13)$, $(-2,-13)$, $(13,2)$, $(-13,-2)$, $(1,26)$, $(26,1)$, $(-1,-26)$, or $(-26,-1)$. Since we're looking for $\square =a^2+b^2$, we just compute $1^2+26^2=677$ and $2^2+13^2=173$, the minimum of which is $\boxed{173}$.