Factor 16x^2+8x+1

Problem

16*x2+8*x+1

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x2+b*x+c

2. Recognize that the first term 16*x2 is a perfect square, (4*x)2 and the last term 1 is also a perfect square, 1

3. Check if the middle term 8*x fits the pattern 2*a*b for the perfect square trinomial formula a2+2*a*b+b2=(a+b)2

4. Verify the middle term by calculating 2(4x)(1) = 8x$.

5. Apply the formula for a perfect square trinomial using a=4*x and b=1

Final Answer

16*x2+8*x+1=(4*x+1)2

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