Final answer:
The algebraic proof for an integer n greater than 1 shows that the expression n^2 - (n - 2)^2 - 2 simplifies to 4n - 6, not n^2. There appears to be an error in the initial claim or question.
Step-by-step explanation:
To prove algebraically that for an integer n greater than 1, the expression n2 - (n - 2)2 - 2 is equal to n2, we first expand the squares and simplify.
Start by expanding (n - 2)2:
(n - 2)2 = n2 - 4n + 4.
Substitute this back into the original expression:
n2 - (n2 - 4n + 4) - 2.
Simplify the expression by distributing the negative sign and subtracting 2:
n2 - n2 + 4n - 4 - 2 = 4n - 6.
However, the claim that this expression equals n2 is incorrect, as the simplification process results in 4n - 6, not n2. There must be an error in the initial assumption or question as it stands.