Answer :

Given: 509^{2} = (500 + 9)^{2} = (500)^{2} + 2(500)(9) + (9)^{2}

= 2500 + 9000 + 81, where a = 500 and b = 9 in the identity (a + b)^{2} = a^{2} + 2ab + b^{2}

= 11581

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