Factor 25x^2+10x+1

Problem

25*x^2+10*x+1

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=25 b=10 and c=1

2. Recognize that the first term 25*x^2 is a perfect square, (5*x)^2 and the last term 1 is also a perfect square, 1^2

3. Check if the middle term 10*x fits the pattern 2*a*b for a perfect square trinomial a^2+2*a*b+b^2

4. Verify the middle term by calculating $2(5x)(1) = 10x$, which matches the given expression.

5. Apply the perfect square trinomial formula a^2+2*a*b+b^2=(a+b)^2 using a=5*x and b=1

Final Answer

25*x^2+10*x+1=(5*x+1)^2

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