Step 1 :The given expression is a quadratic expression of the form \(ax^2 + bx + c\).
Step 2 :To factorize it, we need to find two numbers that add up to -8 (the coefficient of d) and multiply to 16 (the constant term).
Step 3 :The numbers that satisfy these conditions are -4 and -4 because -4 + -4 = -8 and -4 * -4 = 16.
Step 4 :So, the factorization of the given expression is: \(d^2 - 8d + 16 = (d - 4)(d - 4)\).
Step 5 :So, the factored form of \(d^2 - 8d + 16\) is \(\boxed{(d - 4)^2}\).