Question

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

3b2+30b−48
3 b squared plus 30 b minus 48

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

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

3b2+18b−48

Answer 1

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

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

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

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