Question

Multiply the polynomial (b+8)(3b−6)
(
𝑏
+
8
)
(
3
𝑏
−
6
)
to simplify.(1 point)
Responses

b2+18b−36
𝑏
2
+
18
𝑏
−
36
b squared plus 18 b minus 36

3b2+18b−48
3
𝑏
2
+
18
𝑏
−
48
3 b squared plus 18 b minus 48

3b2+30b−48
3
𝑏
2
+
30
𝑏
−
48
3 b squared plus 30 b minus 48

b2+30b−48

Answer 1

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

1. Multiply the first terms:
\[
b \cdot 3b = 3b^2
\]

2. Multiply the outer terms:
\[
b \cdot (-6) = -6b
\]

3. Multiply the inner terms:
\[
8 \cdot 3b = 24b
\]

4. Multiply the last terms:
\[
8 \cdot (-6) = -48
\]

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

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

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