Question 975025
(2x+1)(x+4) and (x+9)(x+9) areas of two rectangles.
{{{2x^2+9x+4}}}  and  {{{x^2+18x+81}}}, their areas.


Which area is greater?


Could the areas be equal?
{{{2x^2+9x+4-x^2-18x-81=0}}}
{{{x^2-9x-77=0}}}
Discriminant, 81+4*77=389, a POSITIVE prime number.


Could the areas be unequal?  Yes.  Which rectangle has greater area depends on x, which is still a variable.
{{{graph(300,300, -30,30,-30,30,x^2-9x-77)}}}


How much greater is one rectangle than the other?
Again, this is variable, depending on x, as long as x is not either root in the "equal" equation.  The best you can give for how much greater is {{{abs(x^2-9x-77)}}}.  For x between the roots, the first rectangle is of lesser area; for x outside the interval bounding the roots, the first rectangle is of greater area.