To express \(x^2 - 4x + 8\) in the form \((x-a)^2 + b\), we complete the square:

1. Start with the expression: \(x^2 - 4x + 8\).

2. Take the coefficient of \(x\), which is \(-4\), halve it to get \(-2\), and square it to get \(4\).

3. Add and subtract \(4\) inside the expression:

\(x^2 - 4x + 4 - 4 + 8\)

4. Rewrite as a perfect square and simplify:

\((x-2)^2 + 4\)