Simplify the following:

(x - 2y - 5)(x - 2y + 3)

Let (x - 2y) = z

Then the given expression = (z - 5)(z + 3)

We know that (x - a)(x + b) = x² - (a - b)x - ab

∴ (z - 5)(z + 3) = z² - (5 - 3)z - (5)(3)

= z² - 2z - 15

= (x - 2y)² - 2(x - 2y) - 15

= (x)² - 2(x)(2y) + (2y)² - 2x + 4y - 15

= x² - 4xy + 4y² - 2x + 4y - 15