We know some facts here:
[tex]W= x-32 \\ \\ H=3x+x^3 \\ \\ \\ Where: \\ \\ W:Width \\ \\ H:Height[/tex]
The perimeter of a rectangle is the total distance around it and the formula is given by:
[tex]P=2W+2H \\ \\ P=2(W+H) \\ \\ \\ Substituting \ values: \\ \\ P=2(x-32+3x+x^3) \\ \\ P=2x-2(32)+2(3x)+2(x^3) \\ \\ P=2x-64+6x+2x^3 \\ \\ \\ \text{Combining like terms:} \\ \\ P=2x^3+(2x+6x)-64 \\ \\ \boxed{P=2x^3+8x-64}[/tex]
