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

Question

Responses

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

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

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

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

Answer 1

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

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

Now, calculate each term:

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

Combine these results:

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

Now combine like terms:

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

So, the simplified result is:

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