The given function is:

\[
p(x) = 4(5x + 6)
\]

### Step-by-step Solution:

To simplify \( p(x) \), distribute the \( 4 \) across the terms inside the parentheses:

\[
p(x) = 4 \cdot (5x) + 4 \cdot (6)
\]
\[
p(x) = 20x + 24
\]

Thus, the simplified form of the function is:

\[
p(x) = 20x + 24
\]

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:

1. How do you evaluate \( p(x) \) for a specific value of \( x \)?
2. What happens if you set \( p(x) = 0 \) and solve for \( x \)?
3. How do you find the derivative of \( p(x) \)?
4. Can you graph \( p(x) = 20x + 24 \) and describe its slope and y-intercept?
5. What if the function was \( p(x) = 4(5x + 6)^2 \)? How would it change?

**Tip**: Distributive property is a key tool for simplifying expressions like \( a(b + c) = ab + ac \).

Learn how to simplify the linear function p(x) = 4(5x + 6) using the distributive property. This step-by-step solution is suitable for students in Grades 6-8 and covers key algebraic concepts such as distributing and combining like terms.

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