Question

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

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

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

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

3b2+18b−48

Answer 1

To simplify the polynomial \((b + 8)(3b - 6)\), we can 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 terms:
\[
3b^2 - 6b + 24b - 48
\]

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

So, the simplified polynomial is:
\[
3b^2 + 18b - 48
\]

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