Respuesta :

roohafzah

expand

  • (2n + 7)^2 = (2n + 7)(2n + 7) = 4n^2 + 28n + 49
  • (2n - 7)^2 = (2n - 7)(2n - 7) = 4n^2 - 28n + 49

perform operations

  • (4n^2 + 28n + 49) - (4n^2 - 28n + 49)
  • 4n^2 - 4n^2 + 28n + 28n +49 - 49
  • 56n

factor out 8 from the above expression

  • 8(7n)

since ,56n can be written as a product of 8 and 7n which is an integer for all the positive values of n , therefore, (2n + 7)² - (2n-7)² is indeed a multiple of 8 for all positive integer values of n.

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