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.