SOLUTION: Please help me factor completely. Thanks! 49r^2+81s^2

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Question 63772: Please help me factor completely. Thanks!
49r^2+81s^2
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You have probably noticed that this the sum of two squares: 49r%5E2+%2B+81s%5E2+=+%287r%29%5E2+%2B+%289s%29%5E2
The sum of two squares has no rational factors, rather, its factors are complex conjugates:
a%5E2+%2B+b%5E2+=+%28a%2Bbi%29%28a-bi%29 where: i+=+sqrt%28-1%29, so:
49r%5E2+%2B+81s%5E2+=+%287r-9si%29%287r%2B9si%29 where: i+=+sqrt%28-1%29