Factor 49x^2+14x+1

Problem

49*x^2+14*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 49*x^2 is a perfect square, as (7*x)^2=49*x^2

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

4. Check if the middle term 14*x fits the pattern 2*a*b for the perfect square trinomial formula a^2+2*a*b+b^2=(a+b)^2

5. Verify the middle term by calculating $2(7x)(1) = 14x$, which matches the given expression.

6. Apply the perfect square trinomial formula where a=7*x and b=1

Final Answer

49*x^2+14*x+1=(7*x+1)^2

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