Multiply the polynomial expression

Question

(b+8)(3b-6)

Answer 1

To multiply the polynomial expression \((b + 8)(3b - 6)\), 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 the terms: \[ 3b^2 - 6b + 24b - 48 \]

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

Thus, the product of the polynomial expression \((b + 8)(3b - 6)\) is: \[ \boxed{3b^2 + 18b - 48} \]