Multiply the polynomial $(b+8)(3b-6)$ to simplify. (1 point)

Question

$b^{2}+30b-48$
$b^{2}+18b-36$
$3b^{2}+30b-48$
$3b^{2}+18b-48$

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: \[ \boxed{3b^2 + 18b - 48} \]