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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. Multiply the first terms: \(b \cdot 3b = 3b^2\)
2. Multiply the outer terms: \(b \cdot (-6) = -6b\)
3. Multiply the inner terms: \(8 \cdot 3b = 24b\)
4. Multiply the last terms: \(8 \cdot (-6) = -48\)
Now combine all the terms:
\[
3b^2 + (-6b) + 24b - 48
\]
Combine the like terms:
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]
So, the simplified polynomial is:
\[
3b^2 + 18b - 48
\]
The correct response is:
**3b² + 18b − 48**.