(b) \( x^{2}-8 x+16= \)

This equation can be identified as a perfect square trinomial. It factors neatly into \( (x - 4)^2 = 0 \). This means the solution would be \( x = 4 \), which makes it a special case since there’s only one unique solution, often referred to as a double root! In practical applications, perfect square trinomials arise frequently in areas like physics for calculating trajectories or optimizing problems. Knowing how to identify and solve these quadratics can save time and minimize mistakes, especially in complex scenarios where simplifications can lead to quicker conclusions. So next time you spot one, grab that opportunity to factor and find solutions for your equations!