Factor by using the perfect-square trinomial formula. \( x^{2}+2 x+1 \)

Did you know that the expression \( x^{2}+2x+1 \) is the result of squaring a binomial? In this case, it factors to \( (x+1)^{2} \). The reason it works is that the middle term (2x) is actually double the product of the binomial's roots (1 and 1), making it a perfect square. When factoring, just remember that looking for perfect squares can save you lots of time! Check if the first and last terms are perfect squares, and if you can find a middle term that’s twice the product of the roots, you’ve likely got a perfect-square trinomial on your hands. Happy factoring!