Factorization 一題~~~

If i understand your question...
[(x^2){y*(n-1)}]/64+ {y*(n+1)}/9 - (xy*n)/12
=[(x^2){y*(n-1)}]/(2^6)+{y^(n+1)}/(3^2)-(xy^n)/(2^2x3)
=[9(x^2){y^(n-1)}+64y^(n+1)-48xy^n]/(3^2x2^6)
={y^(n-1)(9x^2-48xy+64y^2)}/576
={y^(n-1)}{(3x-8y)^2}/576
={y^n(3x-8)^2}/576y //

(1/64)(x^2) * y^(n-1) + (1/9) y^(n+1) - (1/12)xy^n

= [y^(n-1)] * [ (x^2)/64 + (y^2)/9 - xy/12]

= [y^(n-1)] * [ (x/8)^2 + (y/3)^2 - 2(x/8)(y/3)]

= [y^(n-1)] [ (x/8 - y/3)^2 ]