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Out of the given responses, one of the factors of (a2 - b2)3 + (b2 - c2)3 + (c2 - a2)3 is
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- (a + b) (a – b)
- (a + b) (a + b)
- (a – b) (a – b)
- (b – c) (b – c)
- (a + b) (a – b)
Correct Option: A
a2 - b2 + b2 - c2 + c2 - a2 = 0
[ If x + y + z = 0 , x3 + y3 + z3 = 3xyz ]
∴ (a2 - b2)3 + (b2 - c2)3 + (c2 - a2)3 = 3(a2 - b2)(b2 - c2)(c2 - a2)
⇒ (a2 - b2)3 + (b2 - c2)3 + (c2 - a2)3 = 3 (a + b) (a – b) (b + c) (b – c) (c + a) (c – a)
