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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):
\[
(b + 8)(3b - 6) = b \cdot 3b + b \cdot (-6) + 8 \cdot 3b + 8 \cdot (-6)
\]
Now, let's compute each term:
1. \( b \cdot 3b = 3b^2 \)
2. \( b \cdot (-6) = -6b \)
3. \( 8 \cdot 3b = 24b \)
4. \( 8 \cdot (-6) = -48 \)
Now, combine all the terms:
\[
3b^2 - 6b + 24b - 48
\]
Combine like terms (\(-6b + 24b = 18b\)):
\[
3b^2 + 18b - 48
\]
Thus, the simplified result is:
\[
\boxed{3b^2 + 18b - 48}
\]
So the correct answer is **3b² + 18b - 48**.