Question

Multiply the polynomial (b + 8) (3b - 6) to simplify.
b^2 + 18b - 36
b^2 + 30b - 48
3b^2 + 18b - 48
3b^2 + 30b - 48

Answer 1

To multiply the polynomial \( (b + 8)(3b - 6) \), we will 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 the like terms:

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

Thus, the simplified result is:

\[
\boxed{3b^2 + 18b - 48}
\]