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:

$8D^3 - 48D^2 - 3D + 18$

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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.