To expand \((D-6)(8D^2-3)\), apply the distributive property:

\[
(D-6)(8D^2-3) = D \cdot (8D^2 - 3) - 6 \cdot (8D^2 - 3)
\]

Now, expand each term:

1. **Expanding \(D \cdot (8D^2 - 3)\):**
   \[
   D \cdot 8D^2 = 8D^3
   \]
   \[
   D \cdot (-3) = -3D
   \]
   So, \(D \cdot (8D^2 - 3) = 8D^3 - 3D\).

2. **Expanding \(-6 \cdot (8D^2 - 3)\):**
   \[
   -6 \cdot 8D^2 = -48D^2
   \]
   \[
   -6 \cdot (-3) = 18
   \]
   So, \(-6 \cdot (8D^2 - 3) = -48D^2 + 18\).

Now, combine all terms:

\[
(D-6)(8D^2 - 3) = 8D^3 - 48D^2 - 3D + 18
\]

### Final Answer:
\[
8D^3 - 48D^2 - 3D + 18
\]

Would you like more details or have any questions?

### Related Questions
1. How do you apply the distributive property to polynomial expressions?
2. What are some techniques for simplifying polynomials after expansion?
3. How does factoring relate to expansion in polynomial expressions?
4. How do you handle polynomial division for expressions like this?
5. Can this result be further simplified or factored?

**Tip:** When expanding, always check if terms can be combined or factored afterward for simpler results.

Learn how to expand the polynomial expression (D-6)(8D^2 - 3) using the distributive property. This detailed solution covers polynomial expansion, multiplication, and simplification, helping students in Grades 8-10 understand key algebraic techniques.

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