Factor 36x^2+12x+1

Problem

36*x^2+12*x+1

Solution

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

2. Recognize that the first term 36*x^2 is a perfect square, as (6*x)^2=36*x^2

3. Recognize that the last term 1 is a perfect square, as 1^2=1

4. Check if the middle term 12*x fits the pattern 2*a*b for a perfect square trinomial (a+b)^2=a^2+2*a*b+b^2

5. Verify the middle term by calculating $2(6x)(1) = 12x$, which matches the given expression.

6. Apply the formula for a perfect square trinomial to write the factored form.

Final Answer

36*x^2+12*x+1=(6*x+1)^2

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