Question

Multiply the polynomial (b+8) (3b−6) to simplify.
A) b^2 + 18b - 36
B) 3b^2 + 18b - 48
C) b^2 + 30b - 48
D) 3b^2 + 30 - 48

Answer 1

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

1. Multiply the first terms: \(b \cdot 3b = 3b^2\)
2. Multiply the outer terms: \(b \cdot (-6) = -6b\)
3. Multiply the inner terms: \(8 \cdot 3b = 24b\)
4. Multiply the last terms: \(8 \cdot (-6) = -48\)

Now, combine all these results:

\[
3b^2 - 6b + 24b - 48
\]

Combine like terms:

\[
3b^2 + ( -6b + 24b) - 48 = 3b^2 + 18b - 48
\]

So, the simplified result of multiplying the polynomials is:

\[
3b^2 + 18b - 48
\]

The correct answer is **B) \(3b^2 + 18b - 48\)**.