Multiply the polynomial (b+8)(3b−6)

Question

to simplify.(1 point)
Responses

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

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

3b2+18b−48
3 b squared plus 18 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. Distribute \(b\) to both terms in \(3b - 6\):

   • \(b \cdot 3b = 3b^2\)
   • \(b \cdot (-6) = -6b\)

2. Distribute \(8\) to both terms in \(3b - 6\):

   • \(8 \cdot 3b = 24b\)
   • \(8 \cdot (-6) = -48\)

Now, combine all the terms: \[ 3b^2 - 6b + 24b - 48 \] Combine like terms \(-6b\) and \(24b\): \[ 3b^2 + 18b - 48 \]

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

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