Final answer:
To prove the expression n^2-(n-2)^2-2 algebraically, expand (n-2)^2, subtract it from n^2, and simplify the expression.
Step-by-step explanation:
To prove the expression n^2 - (n-2)^2 - 2, we can simplify it step by step.
1. Start by expanding the square (n-2)^2. This can be done by multiplying (n-2) with itself, giving us n^2 - 4n + 4.
2. Now subtract (n-2)^2 from n^2. This means subtracting n^2 - 4n + 4 from n^2, which results in 4n - 4.
3. Finally, subtract 2 from the expression 4n - 4, giving us the simplified form 4n - 6.
Therefore, the expression n^2 - (n-2)^2 - 2 simplifies to 4n - 6.
In this simplification process, we expanded the square and combined like terms to obtain the final result. By following these steps, we were able to simplify the given expression and arrive at the simplified form 4n - 6.