Multiply the polynomial (b+8)(3b−6)

Question

(
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: \[ \boxed{3b^2 + 18b - 48} \]