To multiply the polynomial \( (b + 8)(3b - 6) \), we will use the distributive property (also known as the FOIL method for binomials).
-
First: Multiply the first terms:
\( b \cdot 3b = 3b^2 \) -
Outer: Multiply the outer terms:
\( b \cdot (-6) = -6b \) -
Inner: Multiply the inner terms:
\( 8 \cdot 3b = 24b \) -
Last: Multiply the last terms:
\( 8 \cdot (-6) = -48 \)
Now, combine all these results:
\[ 3b^2 - 6b + 24b - 48 \]
Combine the like terms:
\[ 3b^2 + ( -6b + 24b ) - 48 = 3b^2 + 18b - 48 \]
Thus, the simplified result is:
\[ \boxed{3b^2 + 18b - 48} \]