Factor 64x^2+16x+1

Problem

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

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=a^2+2*a*b+b^2

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*x^2+16*x+1=(8*x+1)^2

Want more problems? Check here!