To work out the expression \(x^2 - 10x + 25\), let's factor it. 

### Step 1: Identify the quadratic expression
The expression is:
\[
x^2 - 10x + 25
\]

### Step 2: Recognize it as a perfect square
This is a perfect square trinomial. A perfect square trinomial takes the form \(a^2 - 2ab + b^2\), which factors to \((a - b)^2\).

In this case:
- \(a^2 = x^2\), so \(a = x\).
- \(b^2 = 25\), so \(b = 5\).
- The middle term \(-2ab\) should equal \(-10x\), and indeed, \(-2(x)(5) = -10x\).

### Step 3: Factor the trinomial
Given the above, the expression can be factored as:
\[
(x - 5)^2
\]

### Final Answer
The expression \(x^2 - 10x + 25\) factors to:
\[
(x - 5)^2
\]

This is the fully worked-out factorization of the expression.

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Would you like more details or have any questions?

Here are five related questions:
1. How do you identify whether a quadratic expression is a perfect square trinomial?
2. What is the difference between factoring and expanding quadratic expressions?
3. How would you factor \(x^2 - 12x + 36\)?
4. What method would you use if the quadratic was not a perfect square trinomial?
5. How can you verify the factorization is correct?

**Tip:** To verify that you've factored a quadratic expression correctly, try expanding the factors back into the original expression.

Learn how to factorize the quadratic expression x^2 - 10x + 25 by recognizing it as a perfect square trinomial. This detailed step-by-step solution is suitable for students in Grades 8-10 and covers key algebraic concepts, including perfect square trinomials.

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