The given expression is:

\[
x^2 - 10x + 25
\]

This is a quadratic expression. To factor it, we need to find two numbers that multiply to \( 25 \) and add to \( -10 \). The numbers \( -5 \) and \( -5 \) fit this criteria.

So, the expression can be factored as:

\[
(x - 5)(x - 5)
\]

or simply:

\[
(x - 5)^2
\]

This shows that the quadratic expression is a perfect square trinomial.

Would you like further details or have any questions? 

Here are some related questions you might find interesting:

1. What is the significance of a perfect square trinomial in solving quadratic equations?
2. How do you complete the square for a quadratic expression that is not already a perfect square?
3. What is the vertex form of a quadratic equation, and how is it related to factoring?
4. How would you solve the equation \( x^2 - 10x + 25 = 0 \)?
5. How can you graph the quadratic function \( y = x^2 - 10x + 25 \)?

**Tip:** Always check if a quadratic expression can be factored easily by identifying it as a perfect square trinomial or by using the quadratic formula.

Discover how to factor the quadratic expression x^2 - 10x + 25 into a perfect square trinomial. This step-by-step guide explores key algebraic concepts, such as factoring and the significance of perfect square trinomials. Ideal for students in Grades 7-9.

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