Question

Multiply the polynomial $(b+8)(3b-6)$ to simplify. (1 point)
$b^{2}+30b-48$
$b^{2}+18b-36$
$3b^{2}+30b-48$
$3b^{2}+18b-48$

Answer 1

To multiply the polynomial \((b + 8)(3b - 6)\), we will 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, combine all these results together:
\[
3b^2 - 6b + 24b - 48
\]

Next, combine the like terms:
\[
3b^2 + (-6b + 24b) - 48 = 3b^2 + 18b - 48
\]

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