Final answer:
The factored form of the binomial 36x²-121y² is (6x + 11y)(6x - 11y), which is derived by recognizing it as a difference of squares and applying the formula a² - b² = (a + b)(a - b).
Step-by-step explanation:
The binomial 36x²-121y² is a difference of squares because it can be written as (6x)² - (11y)², which follows the pattern a² - b². To factor a difference of squares, we use the formula a² - b² = (a + b)(a - b). In this case, a is 6x and b is 11y, so the factored form will be (6x + 11y)(6x - 11y).