Question 724086
Two numbers, p=xy, and x+y=18, so y=18-x.  Substitute to see p=x(18-x), p=18x-x^2,
{{{highlight(p=-x^2+18x)}}}.


p is a function of x and it has a maximum.  How to solve the rest depends on choosing basic Algebra or choosing Calculus using a derivative.  


Completing the Square:
{{{(18/2)^2=81))).  That would be the square term to add & subtract.

{{{-x^2+18x=(-1)(x^2-18x + 81) +81}}}  (Because when multiply by -1, sign changes).
={{{-1(x-9)^2+81}}}


{{{highlight(p=-1(x-9)^2+81)}}}


ANSWER: The MAXIMUM will be at x=9, where p=81
Note: Some of this solution is NOT being rendered correctly in the system but I DID write it correctly.