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

Question

Responses

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

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

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

3b2+30b−48
3 b squared plus 30 b minus 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. Then, multiply the inner terms: \[ 8 \cdot 3b = 24b \]

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

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

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

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

Therefore, the correct response is: 3b^2 + 18b - 48 (or "3 b squared plus 18 b minus 48").