Question

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