Factor 81x^2+18x+1

Problem

81*x^2+18*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 81*x^2 is a perfect square, as (9*x)^2=81*x^2

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

4. Check if the middle term 18*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 $2(9x)(1) = 18x$, which matches the given expression.

6. Apply the perfect square trinomial formula (a+b)^2

Final Answer

81*x^2+18*x+1=(9*x+1)^2

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