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

Question

Responses

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

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

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

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

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 the terms:

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

Combine the like terms:

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

So, the simplified polynomial is:

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

The correct response is:

3b² + 18b − 48.