Factor 16x^2-40x+25

Problem

16*x^2−40*x+25

Solution

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

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

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

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

5. Apply the formula for a perfect square trinomial (a−b)^2 using a=4*x and b=5

Final Answer

16*x^2−40*x+25=(4*x−5)^2

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