Final answer:
The completely factored form of 16x²-72x+81 is (4x-9)², which is a perfect square trinomial derived from the special product of a binomial squared.
Step-by-step explanation:
The expression 16x²-72x+81 in completely factored form can be found by looking for two binomials that when multiplied together, give the original quadratic equation. To factor a quadratic expression of the form ax² + bx + c, you need to find two numbers that both add up to b (the coefficient of the linear term) and multiply to ac (the product of the coefficients of the quadratic and constant terms).
In this case, the expression is a perfect square trinomial because it can be written as (4x-9)². This is because (-9)*(-9) equals 81 and 2*(4x)*(-9) equals -72x, which are the constant and linear coefficients of the original quadratic equation respectively. The factored form of the expression is a perfect square, which is a special product (a difference or sum raised to the second power).