ab(a-b) + bc (b-c) + Ca(c-a) is equal to
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equal to A^2 B- AB^2 + B^2 C- BC^2 + C^2 A - CA^2 ( expanding or opening brackets)
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Step-by-step explanation:
ab(a-b) + bc (b-c) + Ca(c-a)
=a2b−ab2+b2c−bc2+ac2−a2c
Factor: a2(b−c)−a(b2−c2)+bc(b−c)
=a2(b−x)−a(b−c)(b+c)+bc(b−c)
=(b−c)[a2−a(b+c)+bc]
=(b−c)[a2−ab−ac+bc]
=(b−c)[a(a−b)−c(a−b)]
=(b−c)(a−b)(a−c)
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