express (a-b)³+(b-c)³+(c-a)³ as product of its factor
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Let A = a-b
B = b-c
and, C = c-a
Clearly, A+B+C = a-b + b-c + c-a = 0
We know that If A+B+C = 0
Then, A³ + B³ + C³ = 3ABC
Hence, (a-b)³+(b-c)³+(c-a)³ = 3(a-b)(b-c)(c-a)
B = b-c
and, C = c-a
Clearly, A+B+C = a-b + b-c + c-a = 0
We know that If A+B+C = 0
Then, A³ + B³ + C³ = 3ABC
Hence, (a-b)³+(b-c)³+(c-a)³ = 3(a-b)(b-c)(c-a)
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