## x²-10x+25

### (x-5)²

The given expression is x²-10x+25.

To factorize this expression, we can use the following steps:

Step 1: Identify the factors of the first term, which is x². In this case, it is x and x.

Step 2: Identify the factors of the last term, which is 25. The factors of 25 are 1, 5, and 25.

Step 3: Find two factors of 25 that add up to the middle term coefficient, -10. In this case, the factors are -5 and -5.

Step 4: Replace the middle term, -10x, with the two factors found in step 3, which gives x²-5x-5x+25.

Step 5: Group the expression in pairs and factor out the common factor. Doing so gives (x²-5x) – (5x-25).

Step 6: Factor out the greatest common factor from each group. Doing so gives x(x-5) – 5(x-5).

Step 7: Combine like terms to get the final factored form, which is (x-5)(x-5) or (x-5)².

Therefore, the fully factorized form of the expression x²-10x+25 is (x-5)².

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