Question

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

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

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

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

b2+18b−36

Answer 1

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

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

Calculating 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 these results:

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

Combine the like terms \(-6b\) and \(24b\):

\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]

Thus, the simplified expression is:

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

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