To multiply the polynomials (b + 8)(3b - 6), we can use the distributive property (also known as the FOIL method for binomials):
-
First, multiply the first terms:
\( b \cdot 3b = 3b^2 \) -
Next, multiply the outer terms:
\( b \cdot (-6) = -6b \) -
Then, multiply the inner terms:
\( 8 \cdot 3b = 24b \) -
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:
\[ \boxed{3b^2 + 18b - 48} \]