Factor 16x^2-40xy+25y^2

Problem

16*x2−40*x*y+25*y2

Solution

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

2. Determine the square root of the first term 16*x2 which is 4*x

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

4. Verify the middle term by calculating 2*a*b which is 2(4x)(5y) = 40xy$.

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

Final Answer

16*x2−40*x*y+25*y2=(4*x−5*y)2

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