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LHS = (a - b) (a +b) + (b - c) (b + c) + (c - a) (c + a) = (a 2 - b 2 ) + (b 2 - c 2 ) + (c 2 - a 2 ) = a 2 - b 2 +b 2 - c 2 + c 2 - a 2 = a 2 - a 2 + b 2 - b 2 + c 2 - c 2 = 0 Since, LHS = RHS ∴ (a - b) (a +b) + (b - c) (b + c) + (c - a) (c + a) = 0

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Algebraic Expressions and Identities

Short Answer Type

121.

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(ab + bc)² - 2ab²c

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(a - b) (a +b) + (b - c) (b + c) + (c - a) (c + a) = 0

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

Since, LHS = RHS