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To multiply the polynomials \((b+8)(3b−6)\), 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. **Outer:** Multiply the outer terms:
\(b \cdot (-6) = -6b\)
3. **Inner:** Multiply the inner terms:
\(8 \cdot 3b = 24b\)
4. **Last:** Multiply the last terms:
\(8 \cdot (-6) = -48\)
Now, we combine all these results:
\[
3b^2 - 6b + 24b - 48
\]
Combining like terms (\(-6b + 24b\)):
\[
3b^2 + 18b - 48
\]
So the simplified expression is:
\[
3b^2 + 18b - 48
\]
The answer is **A) 3b^2 + 18b - 48**.