Question

multiply to simplify the polynomial expression (b + 8) (3b - 6)

Answer 1

To simplify the polynomial expression \((b + 8)(3b - 6)\), we can use the distributive property (also known as the FOIL method for binomials).

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

2. **Multiply the outer terms**:
\[
b \cdot (-6) = -6b
\]

3. **Multiply the inner terms**:
\[
8 \cdot 3b = 24b
\]

4. **Multiply the last terms**:
\[
8 \cdot (-6) = -48
\]

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

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

Thus, the simplified expression is:
\[
\boxed{3b^2 + 18b - 48}
\]