SOLUTION: Factor the polynomial completely. {{{x^2-y^2+18y-81}}}

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Question 45878: Factor the polynomial completely.
x%5E2-y%5E2%2B18y-81
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I provided a solution (# 29893) for this problem previously.
Factor completely:
x%5E2-y%5E2%2B18y-81 Group the last four terms.
x%5E2-%28y%5E2-18y%2B81%29 Note the change in sign due to the introduction of the parentheses. Now factor the parentheses.%28y%5E2-18y%2B81%29+=+%28y-9%29%28y-9%29 = %28y-9%29%5E2
x%5E2-%28y-9%29%5E2 You will notice that you now have the difference of two squares which will factor nicely.
x%5E2-%28y-9%29%5E2+=+%28x%2B%28y-9%29%29%28x-%28y-9%29%29 This can be simplified to:
%28x%2By-9%29%28x-y%2B9%29 These are the required factors.