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Value of (a–c)[(a–b)2 +(b–c)2 –(a–b)(b–c)]+(c–a)3 is equal to
(1) 3(a – b) (b – c) (c –a) (2) (a – b) (b – c) (c – a)
(3)(a–b)3 (b–c)3 (c–a)3 (4)None of these
Solution
={(a-b)+(b-c) }{(a - b)^2 + (b - c)^2 - (a - b) (b - c)} + (c - a)^3
(x+y) (x^2 - xy+y^2) =x^3 + y^3
=(a-b)^3 +(b-c)^3 +(a-c) ^3
On solving it further
=0
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