multiply the polynomial (b+8) (3b-6) to simplify 1. b^2+18b-36 2. b^2+30b-48 3. 3b^2+30b-48 4. 3b^2+18b-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).

Here's the step-by-step breakdown:

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

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

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

Looking at the options provided, the correct answer is:

4. \(3b^2 + 18b - 48\).