Problem
Factor the following trinomial completely. \[ x^{2}-2 x+1 \] Select the correct choice below and, if necessary, A. $x^{2}-2 x+1=\square$ B. $x^{2}-2 x+1$ is prime.
Solution
Step 1 ：Factor the following trinomial completely: \(x^{2}-2 x+1\).
Step 2 ：The factored form of the expression is \((x - 1)^{2}\).
Step 3 ：\(\boxed{x^{2}-2 x+1=(x-1)^{2}}\)
