Factor the following trinomial. \[ \begin{array}{l}x^{2}+4 x+4 \\ ([?] x+\square)^{2}\end{array} \]

The given trinomial \(x^{2}+4x+4\) can be factored as \((x+2)^{2}\). This means that the expression can be rewritten as a perfect square, specifically the square of a binomial. Here, both the coefficient of \(x\) and the constant term suggest that taking half of 4 gives us 2, and squaring it confirms that \(2^2 = 4\). To illustrate this further, you can think of how completing the square transforms a standard quadratic into a neat structure. By expressing it as \((x+2)^{2}\), you’re not just simplifying; you’re also revealing the symmetry of the equation. Whenever you're faced with a trinomial in the format \(x^2 + bx + c\), double-check if \(c\) is a perfect square and if \(b\) is twice the square root of \(c\). This will save you time and prevent common mistakes in factoring like overlooking the perfect squares or miscalculating coefficients!