Factor 64x^2+16x+1

Problem

64*x2+16*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 64*x2 is a perfect square, as (8*x)2=64*x2

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

4. Check if the middle term 16*x fits the pattern 2*a*b for a perfect square trinomial (a+b)2=a2+2*a*b+b2

5. Verify the middle term by calculating 2(8x)(1) = 16x$, which matches the given expression.

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

Final Answer

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

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