Factor 4x^2-36x+81

Problem

4*x^2−36*x+81

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=4 b=−36 and c=81

2. Recognize that the first term 4*x^2 is a perfect square, as (2*x)^2=4*x^2

3. Recognize that the last term 81 is a perfect square, as 9^2=81

4. Check if the middle term matches the pattern for a perfect square trinomial a^2−2*a*b+b^2=(a−b)^2

5. Verify the middle term by calculating $2(2x)(9) = 36x$.

6. Apply the formula for a perfect square trinomial using a=2*x and b=9

Final Answer

4*x^2−36*x+81=(2*x−9)^2

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