Case: (x−a)2(x−b)2(x-a)^2(x-b)^2(x−a)2(x−b)2 Include terms for each power: P(x)(x−a)2(x−b)2=Ax−a+B(x−a)2+Cx−b+D(x−b)2\frac{P(x)}{(x-a)^2(x-b)^2}=\frac{A}{x-a}+\frac{B}{(x-a)^2}+\frac{C}{x-b}+\frac{D}{(x-b)^2}(x−a)2(x−b)2P(x)=x−aA+(x−a)2B+x−bC+(x−b)2D Some coefficients may turn out to be zero.