Final answer:
The binomial 25x²-121 is factored by recognizing it as a difference of squares, with the factored form being (5x + 11)(5x - 11).
Step-by-step explanation:
The task is to factor the given binomial 25x²-121. This is a difference of squares because both terms are perfect squares (25x² is the square of 5x and 121 is the square of 11). The factored form of a difference of squares is a² - b² = (a + b)(a - b).
Applying this to the given binomial:
- Determine the square root of each term: √(25x²) = 5x and √(121) = 11.
- Write the factored form using the formula for difference of squares: (5x + 11)(5x - 11).
Thus, the binomial 25x²-121 factors to (5x + 11)(5x - 11).