Given the equation:

\[
p \times q = p^3 - 2pq + q^2
\]

We need to find \( 3 \times 2 \) using this formula. Here, \( p = 3 \) and \( q = 2 \).

Substitute these values into the equation:

\[
3 \times 2 = 3^3 - 2(3)(2) + 2^2
\]

First, calculate each term:
- \( 3^3 = 27 \)
- \( 2(3)(2) = 12 \)
- \( 2^2 = 4 \)

Now substitute them back into the equation:

\[
3 \times 2 = 27 - 12 + 4
\]
\[
3 \times 2 = 19
\]

Therefore, \( 3 \times 2 = 19 \).

Would you like further details or explanations?

Here are 5 related questions:
1. What happens if \( p = q \) in the given equation?
2. How would the result change if the coefficient of \( pq \) were different?
3. Can you derive a general formula for \( p \times q \) from the equation?
4. How would you factor the expression \( p^3 - 2pq + q^2 \)?
5. What if both \( p \) and \( q \) were negative?

**Tip:** Always simplify the terms before performing operations to avoid calculation errors.

Explore how to solve the expression p*q = p³ - 2pq + q² by substituting p=3 and q=2. This detailed step-by-step solution introduces key algebraic concepts and polynomial manipulation. Ideal for students in Grades 9-12.

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