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

Question

Responses

A) 3b^2+18b−48
3 b squared plus 18 b minus 48

B) b^2+30b−48
b squared plus 30 b minus 48

C) 3b^2+30b−48
3 b squared plus 30 b minus 48

D) b^2+18b−36
b squared plus 18 b minus 36

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. First: Multiply the first terms:
   \(b \cdot 3b = 3b^2\)

2. Outer: Multiply the outer terms:
   \(b \cdot (-6) = -6b\)

3. Inner: Multiply the inner terms:
   \(8 \cdot 3b = 24b\)

4. Last: Multiply the last terms:
   \(8 \cdot (-6) = -48\)

Now, we combine all these results: \[ 3b^2 - 6b + 24b - 48 \]

Combining like terms (\(-6b + 24b\)): \[ 3b^2 + 18b - 48 \]

So the simplified expression is: \[ 3b^2 + 18b - 48 \]

The answer is A) 3b^2 + 18b - 48.