Final answer:
The quadratic expression 16p^2-8p+1 is factored completely as (4p - 1)^2, which is a perfect square binomial.
Step-by-step explanation:
The question asks to factor completely the quadratic expression 16p^2-8p+1.
To factor this expression, we look for two numbers that multiply to give the product of the coefficient of the square term (16) and the constant term (1), and also add up to the coefficient of the linear term (-8).
The numbers that fulfill these requirements are -4 and -4. Hence we can express the original quadratic as (4p - 1)^2, which is a perfect square binomial.
Therefore, the factored form of the quadratic expression 16p^2 - 8p + 1 is (4p - 1)^2.