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

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 of these results: \[ 3b^2 - 6b + 24b - 48 \]

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

So, the simplified result of \((b + 8)(3b - 6)\) is: \[ \boxed{3b^2 + 18b - 48} \]