Question

Ques. if a and b are natural numbers and a-b is divisible by 3, then a3-b3 is divisible by:

Answer 1

${x}^{3} - {y}^{3} \\ = (x - y)( {x}^{2} + xy + {y}^{2} )$
So clearly x3 - y3 is divisible by (x-y)

So, if (x-y) is divisible by 3, then x3 - y3 is also divisible by 3.

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