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The given polynomials are \((3x + 2)\) and \((2x - 2)\). To find their product, we will apply the distributive property (also known as the FOIL method when multiplying two binomials):

\[
(3x + 2)(2x - 2)
\]

Step-by-step:

1. Multiply the first terms:
   \[
   3x \cdot 2x = 6x^2
   \]

2. Multiply the outer terms:
   \[
   3x \cdot (-2) = -6x
   \]

3. Multiply the inner terms:
   \[
   2 \cdot 2x = 4x
   \]

4. Multiply the last terms:
   \[
   2 \cdot (-2) = -4
   \]

Now, combine all the terms:

\[
6x^2 - 6x + 4x - 4
\]

Simplify by combining like terms:

\[
6x^2 - 2x - 4
\]

Thus, the product of the polynomials \((3x + 2)\) and \((2x - 2)\) is:

\[
6x^2 - 2x - 4
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you multiply two polynomials of higher degrees?
2. What is the FOIL method, and when is it typically used?
3. How do you factor polynomials like the one we just obtained?
4. What is the significance of combining like terms?
5. How does polynomial multiplication relate to quadratic functions?

**Tip:** Always remember to organize your terms by degree (from highest to lowest) when writing the final expression of a polynomial product.

Find the product of the polynomials (3x + 2) and (2x - 2).

Learn how to multiply the polynomials (3x + 2) and (2x - 2) using the distributive property (FOIL method). This problem is suitable for students in Grades 7-9 and covers core algebra concepts.

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