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

Question

Responses

Answer 1

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

1. First, multiply the first terms:
   \( b \cdot 3b = 3b^2 \)

2. Next, multiply the outer terms:
   \( b \cdot (-6) = -6b \)

3. Then, multiply the inner terms:
   \( 8 \cdot 3b = 24b \)

4. Finally, multiply the last terms:
   \( 8 \cdot (-6) = -48 \)

Now, combine all these results:

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

Combine the like terms (\(-6b + 24b\)):

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

So, the simplified result of multiplying the polynomials (b + 8)(3b - 6) is:

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