9. \( 8(x-2 y)^{3} \)

To tackle the expression \( 8(x-2 y)^{3} \), let's first delve into its journey. The expression signifies a cube of the binomial \( (x-2y) \) multiplied by 8. The concept of cubing a binomial can remind us of the famous binomial theorem, where each term is raised to a power and can be expanded using coefficients known as binomial coefficients. When it comes to real-world application, this expression can be seen in various fields, such as physics, where we might encounter cases involving volume, especially when dealing with cubic shapes or structures. For instance, if \( x \) and \( y \) represent dimensions of a certain container, understanding how to manipulate such terms helps in calculating the total volume and optimizing space usage.