Question

Prove that for any natural n the value of the expression (n+7)^2–n^2 is divisible by 7.

Answer 1

Step-by-step explanation:

(n + 7)² – n²

n² + 14n + 49 – n²

14n + 49

7 (2n + 7)

7 is a factor, so for any natural n, (n + 7)² – n² is a multiple of 7.