Asked by PJ
Multiply the polynomials and simplify: (b+8)(3b−6) (1 point)
Responses
b2+30b−48b squared plus 30 b minus 48
3b2+30b−483 b squared plus 30 b minus 48
b2+18b−36b squared plus 18 b minus 36
3b2+18b−48
Responses
b2+30b−48b squared plus 30 b minus 48
3b2+30b−483 b squared plus 30 b minus 48
b2+18b−36b squared plus 18 b minus 36
3b2+18b−48
Answers
Answered by
GPT-4o mini
To multiply the polynomials \( (b + 8)(3b - 6) \), you can use the distributive property (also known as the FOIL method for binomials):
1. **First terms**: \( b \cdot 3b = 3b^2 \)
2. **Outer terms**: \( b \cdot (-6) = -6b \)
3. **Inner terms**: \( 8 \cdot 3b = 24b \)
4. **Last terms**: \( 8 \cdot (-6) = -48 \)
Now, combine these results:
\[
3b^2 - 6b + 24b - 48
\]
Combine the like terms \(-6b\) and \(24b\):
\[
3b^2 + 18b - 48
\]
So the final result after multiplying and simplifying is:
\[
3b^2 + 18b - 48
\]
The correct response is:
**3b² + 18b - 48**
1. **First terms**: \( b \cdot 3b = 3b^2 \)
2. **Outer terms**: \( b \cdot (-6) = -6b \)
3. **Inner terms**: \( 8 \cdot 3b = 24b \)
4. **Last terms**: \( 8 \cdot (-6) = -48 \)
Now, combine these results:
\[
3b^2 - 6b + 24b - 48
\]
Combine the like terms \(-6b\) and \(24b\):
\[
3b^2 + 18b - 48
\]
So the final result after multiplying and simplifying is:
\[
3b^2 + 18b - 48
\]
The correct response is:
**3b² + 18b - 48**