c. \( 16 s^{2}+36 t^{2}= \)

To factor the expression \( 16s^{2} + 36t^{2} \), notice that both components can be rewritten in terms of perfect squares. You can observe that \( 16s^{2} \) is \( (4s)^{2} \) and \( 36t^{2} \) is \( (6t)^{2} \). This gives us a hint that the expression can represent a sum of squares, but it doesn't factor over the real numbers. However, if you wanted to express it as the sum of squares, it can be written as \( (4s)^{2} + (6t)^{2} \). This form is helpful in certain contexts, such as completing the square or when dealing with geometry-related problems like ellipses! Also, if you’re looking at real-world applications, expressions like this pop up more often than you think! For instance, in physics, the sum of squares is crucial when calculating resultant forces. Say you have two forces acting at right angles to one another; you'd use this concept to find the net force using the Pythagorean theorem!