The simplified expression for the given polynomial is:

$u(8u^2v^4 - 16uv^2 + 17)$

Would you like further details or have any questions about this simplification?

Here are some related questions:

1. How do you combine like terms in polynomials?
2. What is the process of factoring a polynomial like this?
3. How can this expression be used to solve for specific values of $u$ and $v$?
4. What are the key properties of polynomials with multiple variables?
5. How can you graph expressions involving multiple variables like this one?

Tip: Always combine terms with the same powers of variables first when simplifying polynomials.