Factor 25x^2-60x+36

Problem

25*x^2−60*x+36

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a^2−2*a*b+b^2

2. Determine the square root of the first term 25*x^2 which is 5*x

3. Determine the square root of the last term 36 which is 6

4. Verify the middle term by calculating 2*(5*x)*(6) which equals 60*x

5. Apply the formula for a perfect square trinomial (a−b)^2

Final Answer

25*x^2−60*x+36=(5*x−6)^2

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