Factor x^2-18x+81

Problem

x^2−18*x+81

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=1 b=−18 and c=81

2. Recognize that the expression is a perfect square trinomial because the first term is x^2 the last term is 9^2 and the middle term is 2⋅x⋅(−9)

3. Apply the formula for a perfect square trinomial, which states that a^2−2*a*b+b^2=(a−b)^2

4. Substitute a=x and b=9 into the formula to get (x−9)^2

Final Answer

x^2−18*x+81=(x−9)^2

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