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

Answer 1

To multiply the polynomial \((b + 8)(3b - 6)\), 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, combine all the results:
\[3b^2 - 6b + 24b - 48\]

Combine the like terms:
\[-6b + 24b = 18b\]

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