The given function is:

$g(p) = 3p(4 - 5p)$

We can expand this expression by applying the distributive property:

$g(p) = 3p \cdot 4 - 3p \cdot 5p$

$g(p) = 12p - 15p^2$

Thus, the expanded form of the function is:

$g(p) = -15p^2 + 12p$

Would you like further details on this, or do you have any questions?

Here are some related questions for practice:

1. What is the derivative of $g(p)$?
2. What are the roots of $g(p) = 0$?
3. What is the value of $g(p)$ when $p = 1$?
4. How would the function behave as $p$ increases indefinitely?
5. What is the vertex of the parabola formed by $g(p) = -15p^2 + 12p$?

Tip: When working with functions, expanding them makes it easier to analyze their behavior and properties like roots, turning points, and end behavior.