Factor 25x^2-20xy+4y^2

Problem

25*x^2−20*x*y+4*y^2

Solution

1. Identify the expression as a trinomial that may fit the pattern of a perfect square trinomial, which follows the form a^2−2*a*b+b^2=(a−b)^2

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

3. Determine the square root of the last term 4*y^2 which is 2*y Let b=2*y

4. Verify the middle term by calculating 2*a*b

2*(5*x)*(2*y)=20*x*y

Since the middle term in the expression is −20*x*y it matches the pattern −2*a*b

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

(5*x−2*y)^2

Final Answer

25*x^2−20*x*y+4*y^2=(5*x−2*y)^2

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