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

Question

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

Answer 1

To multiply the polynomials \( (b+8)(3b-6) \), we can use the distributive property (also known as the FOIL method for binomials):

1. Multiply \( b \) by each term in the second polynomial:

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

2. Multiply \( 8 \) by each term in the second polynomial:

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

Now combine all the terms:

• \( 3b^2 - 6b + 24b - 48 \)

Combine 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