Question 60435
Area of the original piece of cardboard is {{{x^2}}}.

Area of the hole is {{{(x-3)^2 =x^2 - 6x + 9}}}

So the difference between these is 
{{{x^2 - (x^2 -6x + 9) = x^2 - x^2 + 6x - 9 = 6x - 9 }}}


The area of the cardboard left after the hole is cut out is therefore 6x - 9