Factor 36x^2-60x+25

Problem

36*x2−60*x+25

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a2−2*a*b+b2

2. Determine the square roots of the first and last terms.

3. Calculate the first term as a square:

36*x2=(6*x)2

4. Calculate the last term as a square:

25=5

5. Verify the middle term by checking if it equals 2*a*b

2*(6*x)*(5)=60*x

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

(6*x−5)2

Final Answer

36*x2−60*x+25=(6*x−5)2

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