Multiply the polynomial left parenthesis b plus 8 right parenthesis left parenthesis 3 b minus 6 right parenthesis to simplify.

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 in each binomial: \[ b \cdot 3b = 3b^2 \]

2. Outer: Multiply the outer terms: \[ b \cdot (-6) = -6b \]

3. Inner: Multiply the inner terms: \[ 8 \cdot 3b = 24b \]

4. Last: Multiply the last terms in each binomial: \[ 8 \cdot (-6) = -48 \]

Now, combine all these results: \[ 3b^2 - 6b + 24b - 48 \]

Next, combine the like terms: \[ -6b + 24b = 18b \]

Thus, the simplified expression is: \[ \boxed{3b^2 + 18b - 48} \]