To factor the expression x^3 - 4x^2 - 9x + 36, we can use the Rational Root Theorem to find possible rational roots. The possible rational roots are factors of the constant term (36) divided by factors of the leading coefficient (1).

The factors of 36 are ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, and ±36.
The factors of 1 are ±1.

Therefore, the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, and ±36.

By testing these possible roots, we find that x = 3 is a root of the equation. Using synthetic division, we can divide the polynomial by (x - 3):

3 | 1 - 4 - 9 36
| 3 -3 18
-------------
1 - 1 - 12 54

The result is x^2 - x - 12 = (x - 3)(x + 4).

Therefore, x^3 - 4x^2 - 9x + 36 = (x - 3)(x + 4)(x - 1).

To factor the expression x^2 - y^2 - 2x - 2y, we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).

In this case, a = x and b = y. Therefore, we have:

x^2 - y^2 - 2x - 2y = (x + y)(x - y) - 2(x + y) = (x + y)(x - y - 2).

Therefore, x^2 - y^2 - 2x - 2y = (x + y)(x - y - 2).