(1)8a^3b^2-12ab^3c
=4ab²(2a²-3bc)
(2)10a^2b+5ab^2-15ab
=5ab(2a+b-3)
(3)(2a+b)^2-(a-2b)^2
=(2a+b-a+2b)(2a+b+a-2b)
=(a+3b)(2a-b)
(4)x^2-4(x-1)
=x²-4x+4
=(x-2)²
(5)x^2-a^4
=(x-a²)(x+a²)
(6)x^2(a-b)+(b-a)
=(a-b)(x²-1)
=(a-b)(x-1)(x+1)