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

Question

Responses

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

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

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

b2+18b−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).

\[ (b + 8)(3b - 6) = b(3b) + b(-6) + 8(3b) + 8(-6) \]

Calculating each term:

1. \(b \cdot 3b = 3b^2\)
2. \(b \cdot -6 = -6b\)
3. \(8 \cdot 3b = 24b\)
4. \(8 \cdot -6 = -48\)

Now, combine these results:

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

Combine the like terms \(-6b\) and \(24b\):

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

Thus, the simplified expression is:

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

The correct response is 3b² + 18b - 48.