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

Problem

4*x2−20*x*y+25*y2

Solution

1. Identify the structure of the expression as a trinomial that may be a perfect square trinomial of the form a2−2*a*b+b2

2. Determine the square root of the first term 4*x2 which is 2*x

3. Determine the square root of the last term 25*y2 which is 5*y

4. Verify the middle term by calculating 2*(2*x)*(5*y) which equals 20*x*y

5. Apply the formula for a perfect square trinomial a2−2*a*b+b2=(a−b)2 using a=2*x and b=5*y

Final Answer

4*x2−20*x*y+25*y2=(2*x−5*y)2

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