### Instruction: The product of two positive numbers is 24, and the sum of their squares is 73. What is the square of their difference?### Response: I notice that this problem involves a product, a sum of squares, and a square of a difference.
I wonder if I can use some algebraic identities to simplify the expressions.
I recall that (a+b)^2 = a^2 + 2ab + b^2 and (a-b)^2 = a^2 - 2ab + b^2.
I try to apply these identities to the given information.
Let x and y be the two positive numbers, then I have xy = 24 and x^2 + y^2 = 73.
I can write the square of their difference as (x-y)^2 = x^2 - 2xy + y^2.
I see that I can substitute xy = 24 and x^2 + y^2 = 73 into this equation.
I get (x-y)^2 = 73 - 2(24) = 73 - 48 = 25.