The problem is to simplify the expression $(x-2)^2 - x^2$.

1. Problem Description

The problem is to simplify the expression $(x-2)^2 - x^2$.

2. Solution Steps

We need to expand $(x-2)^2$ and then simplify the expression.

The formula for $(a-b)^2$ is:

$(a-b)^2 = a^2 - 2ab + b^2$

In our case, $a = x$ and $b = 2$. Therefore:

$(x-2)^2 = x^2 - 2(x)(2) + 2^2 = x^2 - 4x + 4$

Now we substitute this back into the original expression:

$(x-2)^2 - x^2 = (x^2 - 4x + 4) - x^2$

Next, we simplify the expression by combining like terms:

$x^2 - 4x + 4 - x^2 = x^2 - x^2 - 4x + 4 = -4x + 4$

3. Final Answer

The simplified expression is $-4x + 4$.