Answer:
A
Explanation:
We can factor 625x^4 - 81 by recognizing it as the difference of two squares:
625x^4 - 81 = (25x^2)^2 - 9^2
This can be further simplified using the formula for the difference of squares, which states that:
a^2 - b^2 = (a + b)(a - b)
In this case, a = 25x^2 and b = 9, so we have:
(25x^2 + 9)(25x^2 - 9)
We can then use the difference of squares formula again to factor 25x^2 - 9:
25x^2 - 9 = (5x)^2 - 3^2 = (5x + 3)(5x - 3)
Substituting this into our original expression, we get:
625x^4 - 81 = (25x^2 + 9)(25x^2 - 9) = (25x^2 + 9)(5x + 3)(5x - 3)
Therefore, the fully factored form of 625x^4 - 81 is (25x^2 + 9)(5x + 3)(5x - 3). Answer: (A) (5x - 3)(5x - 3)(25x² + 9)