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

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Question 44989: 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!
You can factor this expression in steps:
x%5E2-y%5E2%2B18y-81 Group the last three terms.
x%5E2-%28y%5E2-18y%2B81%29 Note the change of signs due to the introduction of the parentheses. You can verify that this is the same as the original expression using the distributive property.
Now factor the trinomial in the parentheses.
%28y%5E2-18y%2B81%29+=+%28y-9%29%28y-9%29 = %28y-9%29%5E2 So now you have:
x%5E2-%28y-9%29%5E2 Which, as you can see, is the difference of two squares, and which factors nicely. To wit! A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29, so...
x%5E2-%28y-9%29%5E2+=+%28x%2B%28y-9%29%29%28x-%28y-9%29%29 Simplifying, you get:
%28x%2By-9%29%28x-y%2B9%29 as the factors of the expression x%5E2-y%5E2%2B18y-81