(a^4+b^4)-2a^2b^2 (x^2+9)^2-36x^2 (x^2-2xy+y^2)+(-2x+2y)+1

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(a^4+b^4)-2a^2b^2(x^2+9)^2-36x^2(x^2-2xy+y^2)+(-2x+2y)+1(a^4+b^4)-2a^2b^2(x^2+9)^2-36x^2(x^2-2xy+y^2

(a^4+b^4)-2a^2b^2 (x^2+9)^2-36x^2 (x^2-2xy+y^2)+(-2x+2y)+1
(a^4+b^4)-2a^2b^2 (x^2+9)^2-36x^2 (x^2-2xy+y^2)+(-2x+2y)+1

(a^4+b^4)-2a^2b^2 (x^2+9)^2-36x^2 (x^2-2xy+y^2)+(-2x+2y)+1
(a^4+b^4)-4a^2b^2
=(a^2+b^2-2ab)(a^2+b^2+2ab)
=(a-b)^2(a+b)^2
(x^2+9)^2-36x^2
=(x^2+9-6x)(x^2+9+6x)
=(x-3)^2(x+3)^2
(x^2-2xy+y^2)+(-2x+2y)+1
=(x-y)^2-2(x-y)+1
=(x-y-1)^2