To simplify the expression \((x-3)(3+x)(x-3)(3+x)\), we can first rewrite it for clarity. Notice that \(3 + x\) is the same as \(x + 3\). Therefore, the expression can be rewritten as:

\[
(x-3)(x+3)(x-3)(x+3)
\]

Next, we group the terms:

\[
((x-3)(x+3))^2
\]

Now, we can use the difference of squares formula \(a^2 - b^2 = (a-b)(a+b)\) to simplify \((x-3)(x+3)\):

\[
(x-3)(x+3) = x^2 - 9
\]

Next, we substitute this back into our expression:

\[
((x^2 - 9))^2
\]

Finally, we can expand this square:

\[
(x^2 - 9)^2 = x^4 - 18x^2 + 81
\]

Thus, the simplified expression is:

\[
\boxed{x^4 - 18x^2 + 81}
\]