Question

Multiply the polynomial expression
(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:
\[
\boxed{3b^2 + 18b - 48}
\]