The image contains the following mathematical expression:

$f(x) = x^{2m-1}(a - x)^{2n} \quad \text{in} \quad (0, a)$

This is a function $f(x)$ defined over the interval $(0, a)$, where $a$ is a constant, and the exponents involve $m$ and $n$, which are parameters. Let me know what you'd like to analyze or compute related to this function—such as finding critical points, maximizing/minimizing $f(x)$, or solving related integrals.

Would you like me to:

1. Differentiate $f(x)$ to find critical points or turning points?
2. Analyze the behavior of $f(x)$ over the interval $(0, a)$?
3. Solve for an integral involving $f(x)$?
4. Explore a specific case where $m$ or $n$ has a particular value?
5. Provide insights into the roots or symmetry of $f(x)$?

Tip: When working with functions like $x^p(a-x)^q$, it’s often useful to rewrite the exponents to simplify differentiation or integration tasks.