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Divisibility of x^n +- a^n by x +- a

This type of question, asked 2 times: CDS 2 2020, CDS 2 2022. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    10
    (xn−an)(x^n - a^n) is divisible by (x−a)(x - a), where x≠ax \ne a, for every

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  2. Question 2

    CDS 2 2022

    29
    Consider the question and two statements given below : Question : Is (xn+yn)(x^n + y^n) divisible by (x+y)(x + y) ? Statement-1 : n is a natural number. Statement-2 : n is an even natural number. Which one of the following is correct in respect of the question and the statements ?

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