Question

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

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

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

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

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

Answer 1

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

1. Multiply the first terms: \(b \cdot 3b = 3b^2\)
2. Multiply the outer terms: \(b \cdot (-6) = -6b\)
3. Multiply the inner terms: \(8 \cdot 3b = 24b\)
4. Multiply the last terms: \(8 \cdot (-6) = -48\)

Now, add all these results together:

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

Combine the like terms:

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

Thus, the simplified result is:

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

So the correct response is:

**3b² + 18b - 48** (3 b squared plus 18 b minus 48).