The polynomial $4 a^{6 k} + 36 a^{3 k}b + 81 b^2 - 25 c^{4}$ can be factored into the product of two polynomials, $A \cdot B$ where the coefficient of $c$ in $A$ is less than the coefficient of $c$ in $B$. Find $A$ and $B$.

$A =$
$B =$