Factor 4x^2+4x+1

Problem

4*x^2+4*x+1

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=4 b=4 and c=1

2. Recognize that the first term 4*x^2 is a perfect square, (2*x)^2 and the last term 1 is also a perfect square, 1^2

3. Check if the middle term 4*x matches the pattern for a perfect square trinomial a^2+2*a*b+b^2 where 2*a*b=2*(2*x)*(1)=4*x

4. Apply the perfect square trinomial formula a^2+2*a*b+b^2=(a+b)^2 using a=2*x and b=1

Final Answer

4*x^2+4*x+1=(2*x+1)^2

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