n is an integer greater than 1. Prove algebraically that n^2 – 2 – (n – 2)^2 is always an even number.

1) Expand the brackets: (n-2)² = (n-2)(n-2) = n² - 2n - 2n +4 = n² - 4n + 42) Substitute this into the original expression: n²- 2 - (n² - 4n +4) = n² - 2 - n² + 4n - 4 = 4n - 6 3) Reduce this: 4n - 6 = 2(2n - 3)4) Conclusion: This is always an even number as for all values of n the expression is a multiple of 2