Question

Multiply the polynomial (b+8)(3b−6) to

Answer 1

To multiply the polynomials \( (b + 8)(3b - 6) \), we can use the distributive property (also known as the FOIL method for binomials). Let's perform the multiplication step by step:

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:
\[
3b^2 - 6b + 24b - 48
\]

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

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