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

Question

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

Answer 1

To simplify the polynomial \((b+8)(3b-6)\), we will use the distributive property (also known as the FOIL method for binomials):

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

Now, let's calculate each term:

1. \(b \cdot 3b = 3b^2\)
2. \(b \cdot (-6) = -6b\)
3. \(8 \cdot 3b = 24b\)
4. \(8 \cdot (-6) = -48\)

Now, we combine these results:

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

Next, we combine the like terms \(-6b\) and \(24b\):

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

So, the simplified polynomial is:

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