Question

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, we multiply the first terms:
\[
b \cdot 3b = 3b^2
\]

2. Next, we multiply the outer terms:
\[
b \cdot (-6) = -6b
\]

3. Then, we multiply the inner terms:
\[
8 \cdot 3b = 24b
\]

4. Finally, we multiply the last terms:
\[
8 \cdot (-6) = -48
\]

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

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

The simplified polynomial is:
\[
\boxed{3b^2 + 18b - 48}
\]