Factor x^2-2x+1

Problem

x2−2*x+1

Solution

1. Identify the form of the quadratic expression, which is a*x2+b*x+c where a=1 b=−2 and c=1

2. Recognize that the expression is a perfect square trinomial of the form a2−2*a*b+b2 which factors into (a−b)2

3. Determine the values for the binomial by taking the square root of the first term √(,x2)=x and the square root of the last term √(,1)=1

4. Verify the middle term by checking if 2⋅x⋅1 equals the absolute value of the middle term 2*x

5. Write the factored form as the square of the binomial using the sign of the middle term.

Final Answer

x2−2*x+1=(x−1)2

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