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: Multiply the first terms: \[ b \cdot 3b = 3b^2 \]

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: \[ 8 \cdot (-6) = -48 \]

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

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

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