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.

Learn how to expand and analyze the quadratic function g(p) = 3p(4 - 5p). This solution explains polynomial expansion using the distributive property and provides insights into the behavior of quadratic functions. Suitable for students in Grades 9-11.

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