Factor x^2+2x+1

Problem

x squared plus 2 x plus 1

Solution

1. Identify the form of the quadratic expression, which is a x squared plus b x plus c where a equals 1 b equals 2 and c equals 1

2. Recognize that the expression is a perfect square trinomial of the form a squared plus 2 a b plus b squared which factors into open paren a plus b close paren squared

3. Determine the values for the binomial by taking the square root of the first term the square root of x squared equals x and the square root of the last term the square root of 1 equals 1

4. Verify that the middle term 2 a b matches 2 dollars(x)(1) = 2x$.

5. Write the expression as the square of the binomial open paren x plus 1 close paren

Final Answer

x squared plus 2 x plus 1 equals open paren x plus 1 close paren squared

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