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.