To simplify the expression \( 3x^2(2x^2 + 9x - 6) \), we will distribute \( 3x^2 \) to each term inside the parentheses.

1. Multiply \( 3x^2 \) by \( 2x^2 \):
   \[
   3x^2 \cdot 2x^2 = 6x^4
   \]

2. Multiply \( 3x^2 \) by \( 9x \):
   \[
   3x^2 \cdot 9x = 27x^3
   \]

3. Multiply \( 3x^2 \) by \( -6 \):
   \[
   3x^2 \cdot -6 = -18x^2
   \]

Now, combine all the terms:
\[
6x^4 + 27x^3 - 18x^2
\]

This is the simplified expression.

Do you need more details or have any questions?

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Here are 5 related questions:
1. How do you factor quadratic expressions like \( 2x^2 + 9x - 6 \)?
2. What is the process for factoring polynomials with higher degrees like \( 6x^4 + 27x^3 - 18x^2 \)?
3. How do you apply the distributive property in more complex expressions?
4. Can the expression \( 6x^4 + 27x^3 - 18x^2 \) be factored further?
5. What are the applications of polynomial multiplication in real-world problems?

**Tip:** Always look for common factors in expressions to simplify them further.

Learn how to simplify the polynomial expression 3x^2(2x^2 + 9x - 6) using the distributive property. This step-by-step solution demonstrates multiplying terms inside parentheses by 3x^2, covering algebraic concepts suitable for Grades 9-12.

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