Multiply the polynomial (b+8)(3b−6) to simplify.(1 point) Responses b2+18b−36 b squared plus 18 b minus 36 3b2+30b−48 3 b squared plus 30 b minus 48 b2+30b−48 b squared plus 30 b minus 48 3b2+18b−48 3 b squared plus 18 b minus 48

Answer 1

To multiply the polynomial \((b + 8)(3b - 6)\), we use the distributive property (also known as the FOIL method for binomials).

1. First, distribute \(b\) to both terms in the second polynomial: \[ b \cdot 3b = 3b^2 \] \[ b \cdot (-6) = -6b \]

2. Next, distribute \(8\) to both terms in the second polynomial: \[ 8 \cdot 3b = 24b \] \[ 8 \cdot (-6) = -48 \]

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

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

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

The correct response is: 3b² + 18b - 48.