The expression (x_2 - x_1)^2 + (y_2 - y_1)^2 represents the squared distance between two points in a two-dimensional space. Here, (x_1, y_1) and (x_2, y_2) are the coordinates of these points. The differences (x_2 - x_1) and (y_2 - y_1) calculate how far apart the points are along the x-axis and y-axis, respectively. This formula is derived from the Pythagorean theorem, which relates the sides of a right triangle to its hypotenuse. By squaring the differences and adding them, we find the square of the distance, which can be useful in various applications, such as geometry and computer graphics.