Factor 25x^2-20x+4

Problem

25*x2−20*x+4

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x2+b*x+c

2. Recognize that the first term 25*x2 is a perfect square, (5*x)2 and the last term 4 is also a perfect square, 2

3. Check if the middle term fits the pattern for a perfect square trinomial, a2−2*a*b+b2=(a−b)2

4. Verify the middle term by calculating 2(5x)(2) = 20x$.

5. Apply the formula for a perfect square trinomial since the middle term matches the given expression's middle term of −20*x

Final Answer

25*x2−20*x+4=(5*x−2)2

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