Final answer:
The given polynomial 25x^2-20xy+4y^2 is a perfect square trinomial and can be factored into (5x - 2y)^2.
Step-by-step explanation:
The polynomial 25x^2-20xy+4y^2 is indeed a perfect square trinomial. A perfect square trinomial takes the form (ax)^2 − 2axy − (ay)^2, which can be factored into (ax − ay)^2. In this case, we can identify the square root of the first term as 5x and the square root of the last term as 2y. The middle term is twice the product of these square roots with a negative sign, confirming it's a perfect square.
To factor this, we take the square root of the first and last terms and write them as (5x − 2y), then square the binomial: (5x − 2y)^2. This is the factored form of the given polynomial, showing that it is indeed a perfect square trinomial.