Multiply the polynomial (b + 8) (3b - 6) 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, we multiply the first terms: \[ b \cdot 3b = 3b^2 \]

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

3. Then, we multiply the inner terms: \[ 8 \cdot 3b = 24b \]

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

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

Next, combine the like terms \(-6b\) and \(24b\): \[ 3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48 \]

The simplified polynomial is: \[ \boxed{3b^2 + 18b - 48} \]