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 that the middle term 2*a*b matches 2(x)(1) = 2x$.

5. Write the expression as the square of the binomial (x+1)

Final Answer

x2+2*x+1=(x+1)2

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