Factor 9x^2+6x+1

Problem

9*x^2+6*x+1

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=9 b=6 and c=1

2. Recognize that the expression is a perfect square trinomial because the first term 9*x^2 is (3*x)^2 the last term 1 is (1)^2 and the middle term 6*x is 2*(3*x)*(1)

3. Apply the formula for a perfect square trinomial, which states that a^2+2*a*b+b^2=(a+b)^2

4. Substitute a=3*x and b=1 into the formula to obtain the factored form.

Final Answer

9*x^2+6*x+1=(3*x+1)^2

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