Expand the expression $(x - y - 2z)^2$.

1. Problem Description

Expand the expression $(x - y - 2z)^2$.

2. Solution Steps

We can expand the given expression using the formula for the square of a trinomial:

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$.

In our case, $a = x$, $b = -y$, and $c = -2z$. Substituting these values into the formula, we get:

$(x - y - 2z)^2 = (x + (-y) + (-2z))^2$

$= x^2 + (-y)^2 + (-2z)^2 + 2(x)(-y) + 2(x)(-2z) + 2(-y)(-2z)$

$= x^2 + y^2 + 4z^2 - 2xy - 4xz + 4yz$

3. Final Answer

$x^2 + y^2 + 4z^2 - 2xy - 4xz + 4yz$