(1) \( (x-5)^{2} \)

Did you know that the expression \( (x-5)^{2} \) is a perfect square trinomial? When expanded, it becomes \( x^2 - 10x + 25 \). This form can be particularly useful because it allows you to easily identify key features of the quadratic, such as the vertex, which is at the point \( (5, 0) \). Using this expression in real-life situations, consider a scenario where you're calculating the area of a square with a side length of \( (x-5) \). This concept can be applied in various fields, from architecture to landscaping, where an understanding of area is essential for planning and design.