Multiply the polynomial (b+8)(3b−6)

Question

to simplify.(1 point)
Responses

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

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

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

3b2+18b−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):

\[ (b + 8)(3b - 6) = b \cdot 3b + b \cdot (-6) + 8 \cdot 3b + 8 \cdot (-6) \]

Now, let's compute each term:

1. \( b \cdot 3b = 3b^2 \)
2. \( b \cdot (-6) = -6b \)
3. \( 8 \cdot 3b = 24b \)
4. \( 8 \cdot (-6) = -48 \)

Now, combine all the terms:

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

Combine like terms (\(-6b + 24b = 18b\)):

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

Thus, the simplified result is:

\[ \boxed{3b^2 + 18b - 48} \]

So the correct answer is 3b² + 18b - 48.