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

Question

Responses

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

b2+18b−36
b squared plus 18 b minus 36

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

3b2+30b−48

Answer 1

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. Next, multiply the outer terms:
   \( b \cdot (-6) = -6b \)

3. Now, multiply the inner terms:
   \( 8 \cdot 3b = 24b \)

4. Finally, multiply the last terms:
   \( 8 \cdot (-6) = -48 \)

Now combine all the results:

\[ 3b^2 - 6b + 24b - 48 \]

Combine like terms (\(-6b + 24b\)):

\[ 3b^2 + 18b - 48 \]

So, the simplified form of \( (b + 8)(3b - 6) \) is:

3b^2 + 18b - 48.

The correct response is:

3b^2 + 18b - 48.