The problem asks us to simplify the expression $(x-10y)(x^2 + 10xy + 100y^2)$.

1. Problem Description

The problem asks us to simplify the expression $(x-10y)(x^2 + 10xy + 100y^2)$.

2. Solution Steps

We can use the formula for the difference of cubes:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

In this case, we can set $a = x$ and $b = 10y$. Then, $a - b = x - 10y$ and $a^2 + ab + b^2 = x^2 + x(10y) + (10y)^2 = x^2 + 10xy + 100y^2$.

Thus, the given expression is in the form of the right-hand side of the difference of cubes formula.

So, we have:

$(x - 10y)(x^2 + 10xy + 100y^2) = x^3 - (10y)^3 = x^3 - 1000y^3$.

3. Final Answer

$x^3 - 1000y^3$