Factoring a perfect square trinomial with leading coefficlent 1 Factor. \[ w^{2}+8 w+16 \]

Step 1 ：Define the variable \(w\).

Step 2 ：Define the trinomial \(w^{2}+8 w+16\).

Step 3 ：Define the factored form \((w + 4)^2\).

Step 4 ：Check if the trinomial is equal to the factored form.

Step 5 ：The trinomial \(w^{2}+8 w+16\) is indeed equal to the factored form \((w + 4)^2\). Therefore, the trinomial can be factored into \((w + 4)^2\).

Step 6 ：\(\boxed{(w + 4)^2}\) is the final answer.