Factorize 4(x-y)² -9(x+y)²

To factorize the expression 4(x-y)² - 9(x+y)², we can use the difference of squares formula:

a² - b² = (a + b)(a - b)

First, let's rewrite the expression using this formula:

4(x-y)² - 9(x+y)² = (2(x-y) - 3(x+y))(2(x-y) + 3(x+y))

Now, we can simplify this expression:

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

Therefore, the factored form of 4(x-y)² - 9(x+y)² is:

(-x - 5y)(5x + y)