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To expand the given expression \((4x^2 - 2)(3x + 6)\), we will use the distributive property (also known as the FOIL method in this case, since each expression is a binomial).

### Step-by-Step Expansion:

1. Distribute \(4x^2\) to both terms in \((3x + 6)\):
   \[
   4x^2 \cdot 3x = 12x^3
   \]
   \[
   4x^2 \cdot 6 = 24x^2
   \]

2. Distribute \(-2\) to both terms in \((3x + 6)\):
   \[
   -2 \cdot 3x = -6x
   \]
   \[
   -2 \cdot 6 = -12
   \]

### Combine all the terms:
\[
12x^3 + 24x^2 - 6x - 12
\]

Thus, the expanded form of \((4x^2 - 2)(3x + 6)\) is:
\[
12x^3 + 24x^2 - 6x - 12
\]

Would you like any further clarification or details on this?

### Related Questions:
1. How do you expand binomials with higher powers?
2. What are the rules of the distributive property?
3. How would the result change if the terms were cubed?
4. Can you factor the final result back to its original form?
5. What are some practical applications of expanding algebraic expressions?

**Tip:** Always combine like terms when expanding expressions to simplify your final answer.

Learn how to expand the polynomial expression (4x^2 - 2)(3x + 6) using the distributive property. This problem covers key algebraic concepts and demonstrates how to apply polynomial expansion. Suitable for students in Grades 8-10.

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