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To multiply the polynomial \( (b + 8)(3b - 6) \), we can use the distributive property (also known as the FOIL method for binomials):
1. First, multiply the first terms:
\( b \cdot 3b = 3b^2 \)
2. Next, multiply the outer terms:
\( b \cdot (-6) = -6b \)
3. Now, multiply the inner terms:
\( 8 \cdot 3b = 24b \)
4. Finally, multiply the last terms:
\( 8 \cdot (-6) = -48 \)
Now combine all the results:
\[
3b^2 - 6b + 24b - 48
\]
Combine like terms (\(-6b + 24b\)):
\[
3b^2 + 18b - 48
\]
So, the simplified form of \( (b + 8)(3b - 6) \) is:
**3b^2 + 18b - 48**.
The correct response is:
**3b^2 + 18b - 48**.