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Show that (a – b) (a + b) + (b – c)(b + c) + (c – a) (c + a) = 0.

1 Answer

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Best answer

LHS

(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a)

= (a2 – b2) + (b2 – c2) + (c2 – a2)

= a2 – b2 + b2 – c2 + c2 – a2

= (a2 – a2) + (b2 – b2) + (c2 – c2)

= 0 + 0 + 0 + 0

= RHS

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