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Question
(a − b)3 + (b − c)3 + (c − a)3 =
Options
(a + b + c) (a2 + b2 + c2 − ab − bc − ca)
(a − b) (b − c) (c − a)
3(a − b) ( b− c) (c − a)
none of these
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Solution
Given `(a-b)^3 + (b-c)^3 + (c-a)^2`
Using identity `x^2 +y^3 +z^3 = 3xyz`
Here `x = a -b, y = b -c,z = c-a`
`(a-b)^3 +(b-c)^3 (c-a)^3 = 3(a-b )(b-c)(c-a)`
Hence the Value of `(a-b)^3+ (b-c)^3+(c-a)^3` is `3(a-b)(b-c)(c-a)`
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