The expression x^2 + y^2 represents the sum of the squares of two variables, x and y. This mathematical formula is commonly used in geometry, particularly in the context of the Cartesian coordinate system. It helps describe the distance from the origin to a point (x, y) in a two-dimensional space. In the context of geometry, x^2 + y^2 = r^2 defines a circle with radius r centered at the origin. This relationship illustrates how the values of x and y can vary while still maintaining a constant distance from the center point.