Question

Multiplying Polynomials Quick Check
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Question
Multiply the polynomial (b+8)(3b−6)
to simplify.(1 point)
Responses

b2+18b−36
b squared plus 18 b minus 36

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

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

3b^2+30b−48

Answer 1

To multiply the polynomials \((b+8)(3b−6)\), we use the distributive property (often called FOIL for binomials):

1. First, multiply \(b\) by each term in the second polynomial:
- \(b \cdot 3b = 3b^2\)
- \(b \cdot (-6) = -6b\)

2. Next, multiply \(8\) by each term in the second polynomial:
- \(8 \cdot 3b = 24b\)
- \(8 \cdot (-6) = -48\)

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

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

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

The correct response is:
**3b^2 + 18b - 48** (3 b squared plus 18 b minus 48).