(1)x^4-x^2 (2)a(x^2-y^2)+b(y^2-x^2) (3)-27x^4+18x^3-3x^2 (4)x^4-1 (5)a^4-2a^b^2+b^4(6)(a^2-a)^2-(a-1)^2

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(1)x^4-x^2 (2)a(x^2-y^2)+b(y^2-x^2) (3)-27x^4+18x^3-3x^2 (4)x^4-1 (5)a^4-2a^b^2+b^4(6)(a^2-a)^2-(a-1)^2
(1)x^4-x^2 (2)a(x^2-y^2)+b(y^2-x^2) (3)-27x^4+18x^3-3x^2 (4)x^4-1 (5)a^4-2a^b^2+b^4
(6)(a^2-a)^2-(a-1)^2

(1)x^4-x^2 (2)a(x^2-y^2)+b(y^2-x^2) (3)-27x^4+18x^3-3x^2 (4)x^4-1 (5)a^4-2a^b^2+b^4(6)(a^2-a)^2-(a-1)^2
(1)x^4-x^2
=x^2(x^2-1)
=x^2(x+1)(x-1)
(2)a(x^2-y^2)+b(y^2-x^2)
=(x^2-y^2)(a-b)
=(x+y)(x-y)(a-b)
(3)-27x^4+18x^3-3x^2
=-3x^2(9x^2-6x+1)
=-3x^2(3x-1)^2
(4)x^4-1
=(x^2+1)(x^2-1)
=(x^2+1)(x+1)(x-1)
(5)a^4-2a^b^2+b^4
=(a^2-b^2)^2
=(a+b)^2(a-b)^2
(6)(a^2-a)^2-(a-1)^2
=(a^2-a+a-1)(a^2-a-a+1)
=(a+1)(a-1)(a-1)^2
=(a+1)(a-1)^3