Question

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

b2+18b−36
b squared plus 18 b minus 36

b2+30b−48
b squared plus 30 b minus 48

3b2+18b−48
3 b squared plus 18 b minus 48

3b2+30b−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).

Let's perform the multiplication step-by-step:

1. **Distribute \( b \) to both terms in \( (3b - 6) \)**:
\[
b \cdot 3b = 3b^2
\]
\[
b \cdot (-6) = -6b
\]

2. **Distribute \( 8 \) to both terms in \( (3b - 6) \)**:
\[
8 \cdot 3b = 24b
\]
\[
8 \cdot (-6) = -48
\]

3. **Combine all the results**:
\[
3b^2 - 6b + 24b - 48
\]

4. **Combine like terms**:
\[
3b^2 + ( -6b + 24b) - 48 = 3b^2 + 18b - 48
\]

So, the simplified result is:
\[
3b^2 + 18b - 48
\]

Thus, the correct answer is:
**3b^2 + 18b - 48**