Multiply the polynomial (b+8)(3b−6) to simplify.(1 point) Responses b2+18b−36 b squared plus 18 b minus 36 3b2+30b−48 3 b squared plus 30 b minus 48 b2+30b−48 b squared plus 30 b minus 48 3b2+18b−48 3 b squared plus 18 b minus 48

To multiply the polynomial \((b + 8)(3b - 6)\), we use the distributive property (also known as the FOIL method for binomials).

1. First, distribute \(b\) to both terms in the second polynomial:
\[
b \cdot 3b = 3b^2
\]
\[
b \cdot (-6) = -6b
\]

2. Next, distribute \(8\) to both terms in the second polynomial:
\[
8 \cdot 3b = 24b
\]
\[
8 \cdot (-6) = -48
\]

3. Now, combine all the results:
\[
3b^2 - 6b + 24b - 48
\]

4. Combine like terms (\(-6b\) and \(24b\)):
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]

Thus, the simplified form of \((b + 8)(3b - 6)\) is:
\[
3b^2 + 18b - 48
\]

The correct response is:
**3b² + 18b - 48**.