Question

multiply the polynomial (b+8) (3b-6) to simplify 1. b^2+18b-36 2. b^2+30b-48 3. 3b^2+30b-48 4. 3b^2+18b-48

Answer 1

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

Here's the step-by-step breakdown:

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

So, the simplified result of the polynomial multiplication \((b + 8)(3b - 6)\) is:
\[
3b^2 + 18b - 48
\]

Looking at the options provided, the correct answer is:

**4. \(3b^2 + 18b - 48\)**.