Prove that a²-ab+b²= (a+b)²-3ab
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Your question has been proved in the attachment.
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Taking RHS ,
(a+b)² = a² + 2ab + b²
⇒ (a+b)² - 3ab = (a² + 2ab + b²) - 3ab
⇒ (a+b)² - 3ab = a² + 2ab + b² - 3ab
⇒ (a+b)² - 3ab = a² - ab + b² = LHS
∴ a²- ab + b² = (a+b)² - 3ab
Hence Proved !!!
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