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The expression to simplify is:

\[
7p^2 - \frac{3}{4}(4p - 8) + 2p^2
\]

### Steps to Simplify:

1. **Distribute the \(\frac{3}{4}\) across the terms inside the parentheses**:
   \[
   \frac{3}{4}(4p - 8) = \frac{3}{4} \cdot 4p - \frac{3}{4} \cdot 8 = 3p - 6
   \]
   So the expression becomes:
   \[
   7p^2 - (3p - 6) + 2p^2
   \]

2. **Distribute the negative sign**:
   \[
   7p^2 - 3p + 6 + 2p^2
   \]

3. **Combine like terms**:
   \[
   (7p^2 + 2p^2) - 3p + 6 = 9p^2 - 3p + 6
   \]

Thus, the simplified expression is:

\[
9p^2 - 3p + 6
\]

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Would you like more details or have any questions?

### Related Questions:
1. What is the distributive property in algebra?
2. How do you combine like terms in polynomials?
3. What are the rules for distributing a fraction in an algebraic expression?
4. Can you explain how negative signs affect distribution?
5. How do you recognize and simplify quadratic expressions?

**Tip:** Always distribute and combine terms carefully to avoid errors, especially when negative signs are involved.

Which expression is equivalent to: 7p^2 - (3/4)(4p - 8) + 2p^2?

Learn how to simplify the algebraic expression 7p^2 - (3/4)(4p - 8) + 2p^2 with a step-by-step explanation. This problem demonstrates key concepts like the distributive property and combining like terms, suitable for students in Grades 8-10.

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