a(b²-c²)+b²(c²-a²)+c²(a²-b²)
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a(b²-c²)+b(c²-a²)+c(a²-b²)
=ab²-ac²+bc²-a²b+a²c-b²c
=ab²-a²b-ac²+bc²+a²c-b²c
=ab(b-a)-c²(a-b)+c(a²-b²)
=-ab(a-b)-c²(a-b)+c((a+b)(a-b))
=(a-b)[-ab-c²+c(a+b)]
=(a-b)[-ab+cb-c²+ac]
=(a-b)[-b(c-a)-c(c-a)]
=(a-b)(b-c)(c-a
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