Question
Use your result from the previous task to find the sum. \( 6 a b^{2} \) \( 3 a b+3 b^{2} \) \( -6 a^{2}+3 a b+3 b^{2} \) \( -6 a^{2}-13 a b+3 b^{2} \) DONE
Ask by Santiago Reeves.
Feb 06,2025 22:58
UpStudy AI Solution
Tutor-Verified Answer
Answer
The sum of the expressions is \( -12a^{2} - 7a b + 6a b^{2} + 9b^{2} \).
Solution
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Bonus Knowledge
To find the sum of the four expressions given, we will simply combine like terms systematically.
Start with:
1. \( 6ab^2 \)
2. \( 3ab + 3b^2 \)
3. \( -6a^2 + 3ab + 3b^2 \)
4. \( -6a^2 - 13ab + 3b^2 \)
Collecting all the terms, we have:
- **For \(a^2\)**: \( -6a^2 - 6a^2 = -12a^2 \)
- **For \(ab\)**: \( 6ab^2 + 3ab + 3ab - 13ab = 6ab^2 - 7ab \)
- **For \(b^2\)**: \( 6ab^2 + 3b^2 + 3b^2 = 12b^2 \)
Combining these, we get the sum:
\[
-12a^2 - 7ab + 12b^2
\]
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