Multiply the polynomial (b+8)(3b−6)

Question

to simplify.(1 point)
Responses

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

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

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

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

Answer 1

To multiply the polynomial \((b+8)(3b−6)\), you 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, add all these results together:

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

Combine the like terms:

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

Thus, the simplified result is:

\[ 3b^2 + 18b - 48 \]

So the correct response is:

3b² + 18b - 48 (3 b squared plus 18 b minus 48).