Question

Multiply the polynomial (b+8)(3b−6) to simplify.(1 point)
Responses

b2+30b−48
b squared plus 30 b minus 48

3b2+30b−48
3 b squared plus 30 b minus 48

3b2+18b−48
3 b squared plus 18 b minus 48

b2+18b−36

Answer 1

To multiply the polynomials \((b + 8)(3b - 6)\), we can use the distributive property (FOIL method in this case):

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

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

Thus, the simplified polynomial is:
\[
3b^2 + 18b - 48
\]

So the correct response is:
**3b² + 18b - 48** (or "3 b squared plus 18 b minus 48").