A perfect square trinomial is of the form:

$(ax)^2 + 2abx + b^2 = (ax + b)^2$

Let's evaluate each option to see if it fits this form.

(A) $5x^2 - 5x + 1$:

1. The first term is $5x^2$, but this is not a perfect square (5 is not a perfect square).
2. It cannot be written in the form $(ax + b)^2$.

(B) $5x^2 - 10x + 5$:

1. The first term is $5x^2$, which is not a perfect square.
2. It cannot be written in the form $(ax + b)^2$.

(C) $10x^2 - 5x + 5$:

1. The first term is $10x^2$, which is not a perfect square.
2. It cannot be written in the form $(ax + b)^2$.

(D) $25x^2 - 10x + 1$:

1. The first term is $25x^2 = (5x)^2$, which is a perfect square.
2. The last term is $1 = 1^2$, which is a perfect square.
3. The middle term is $-10x$, which can be written as $2 \cdot 5x \cdot (-1)$.

Thus, this can be written as:

$(5x - 1)^2 = 25x^2 - 10x + 1$

This is a perfect square trinomial.

(E) $25x^2 - 25x + 5$:

1. The first term is $25x^2$, which is a perfect square.
2. The last term is 5, which is not a perfect square.

So, option (D) is the only perfect square trinomial.

The answer is:

(D) $25x^2 - 10x + 1$

Would you like more details or have any questions?

Here are 5 related questions:

1. What are the properties of a perfect square trinomial?
2. How do you factor a perfect square trinomial?
3. Can a trinomial be a perfect square if its coefficients are not integers?
4. What are the differences between perfect square trinomials and general trinomials?
5. How can you verify if a given trinomial is a perfect square?

Tip: To quickly identify a perfect square trinomial, check if both the first and last terms are perfect squares, and if the middle term equals twice the product of their square roots.