Let's simplify the expression step-by-step:

The given expression is:

$p^2(q^2 - p) + q(p - q^2)$

Step 1: Distribute the terms in each part

First, distribute $p^2$ over $(q^2 - p)$ and $q$ over $(p - q^2)$.

$p^2(q^2 - p) = p^2 \cdot q^2 - p^2 \cdot p = p^2 q^2 - p^3$ $q(p - q^2) = q \cdot p - q \cdot q^2 = qp - q^3$

Step 2: Combine the terms

Now, combine all the terms we obtained:

$p^2 q^2 - p^3 + qp - q^3$

Thus, the simplified expression is:

$p^2 q^2 - p^3 + qp - q^3$

This is the final simplified form.

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Would you like further explanation or details on any part of the process?

Here are a few related questions you could explore:

1. How do you distribute terms in algebraic expressions?
2. What does factoring do, and when should we use it?
3. How do you identify like terms in an expression?
4. How would you approach simplifying expressions with exponents?
5. Can you simplify more complex expressions that include higher powers?

Tip: Always distribute terms carefully and watch for any common factors when simplifying to avoid missing opportunities for factoring.