Let's simplify the expression:

Given:  
\[ 4p(p + 7) - 8(p - 6) \]

**Step 1: Distribute the terms inside the parentheses.**

- For the first term, distribute \(4p\) across \((p + 7)\):
\[
4p \cdot p + 4p \cdot 7 = 4p^2 + 28p
\]

- For the second term, distribute \(-8\) across \((p - 6)\):
\[
-8 \cdot p - 8 \cdot (-6) = -8p + 48
\]

**Step 2: Combine the results from both distributions:**
\[
4p^2 + 28p - 8p + 48
\]

**Step 3: Combine like terms (terms with \(p\)):**
\[
4p^2 + 20p + 48
\]

So, the simplified expression is:
\[
4p^2 + 20p + 48
\]

Would you like more details on any step or have any questions?

Here are 5 related questions:
1. How do you factor the expression \(4p^2 + 20p + 48\)?
2. What happens if you substitute a specific value for \(p\) in the simplified expression?
3. Can this expression be solved for \(p\) if it equals zero?
4. What are the roots of the quadratic equation formed by setting \(4p^2 + 20p + 48 = 0\)?
5. How does the distributive property apply to binomials?

**Tip:** Always combine like terms after distributing to simplify your expressions accurately.

Learn how to simplify the algebraic expression 4p(p + 7) - 8(p - 6) with step-by-step instructions. This solution covers polynomial expansion using the distributive property and the combination of like terms. Suitable for students in Grades 8-10.

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