Question 45878
I provided a solution (# 29893) for this problem previously.

Factor completely:
{{{x^2-y^2+18y-81}}} Group the last four terms.
{{{x^2-(y^2-18y+81)}}} Note the change in sign due to the introduction of the parentheses.  Now factor the parentheses.{{{(y^2-18y+81) = (y-9)(y-9)}}} = {{{(y-9)^2}}}
{{{x^2-(y-9)^2}}} You will notice that you now have the difference of two squares which will factor nicely.
{{{x^2-(y-9)^2 = (x+(y-9))(x-(y-9))}}} This can be simplified to:
{{{(x+y-9)(x-y+9)}}} These are the required factors.