Let one part = x
other part = (20-x)
their product, p = x(20-x) = 20x - x²
For the product, p to be maximum
So, product is maximum when we divide 20 into 2 parts as (10,10).
Note: If you want to show that dividing 20 into (10,10) yields maximum product, not minimum; find the second derivative of p. If the value of second derivative at x=10 comes as negative, then it is maximum. (It comes -2, so it is maximum).