Final answer:
The difference of two squares, 4y²-25x², is factored as (2y + 5x)(2y - 5x), where 4y² is (2y)² and 25x² is (5x)².
Step-by-step explanation:
Factor the difference of two squares, 4y²-25x².
To factor this expression, we need to recognize that 4y² and 25x² are both perfect squares, and that the expression is a subtraction of one from the other. The difference of two squares has a factoring pattern:
a² - b² = (a + b)(a - b).
Here, 4y² is the square of 2y, and 25x² is the square of 5x. Thus:
(2y)² - (5x)² = (2y + 5x)(2y - 5x).
Therefore, the factored form of 4y²-25x² is (2y + 5x)(2y - 5x).