Find two numbers differing by 44 whose product is as small as possible.

Ans : Let the smallest is equal to x, so the largest is x+44. The product would be equal to x(x+44) = x^2+44x = (x+22)^2 - 484. Since the minimum of the square of any real is 0, the minimum of the (x+22)^2 is 0, too, and the critical value for the x-variable is -22. So, the numbers are -22 and -22+44=22 (the product value is -484)

Distributive property