Multiplying Polynomials Quick Check 1 of 51 of 5 Items Question Multiply the polynomial (b+8)(3b−6) to simplify.(1 point) Responses b2+30b−48 b squared plus 30 b minus 48 b2+18b−36 b squared plus 18 b minus 36 3b2+18b−48 3 b squared plus 18 b minus 48 3b2+30b−48

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

Combine like terms:
\[
3b^2 + 18b - 48
\]

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

Thus, the correct response is **3b² + 18b − 48**.