Multiply the polynomial (b+8)(3b−6)

Question

to simplify.(1 point)
Responses

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

b2+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).

Let's perform the multiplication step by step:

1. First: Multiply the first terms:
   \(b \cdot 3b = 3b^2\)

2. Outer: Multiply the outer terms:
   \(b \cdot (-6) = -6b\)

3. Inner: Multiply the inner terms:
   \(8 \cdot 3b = 24b\)

4. Last: Multiply the last terms:
   \(8 \cdot (-6) = -48\)

Now, combine all these results: \[ 3b^2 - 6b + 24b - 48 \] Combine the like terms (\(-6b + 24b\)): \[ 3b^2 + 18b - 48 \]

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

So, the correct response is: 3b² + 18b - 48.