Factorize the following trinomial square: \(x^2 - 6x + 9\)

Step 1 ：First, to factor a trinomial square, we need to identify if the given trinomial can be expressed as \((a-b)^2\). This is the case if and only if the trinomial can be written in the form \(a^2 - 2ab + b^2\).

Step 2 ：Here, the given trinomial is \(x^2 - 6x + 9\). We can see that \(x^2\) is \(a^2\), \(-6x\) is \(-2ab\), and \(9\) is \(b^2\). The values of \(a\) and \(b\) are then \(x\) and \(3\) respectively.

Step 3 ：Therefore, the trinomial \(x^2 - 6x + 9\) can be factored as \((x - 3)^2\).