Answer
(a) $40x^{2}+240x+200$
(b) $57600\,ft^{2}$
Work Step by Step
(a) $\text{Area}=(4x+20)(10x+10)$
Using FOIL (First Outer Inner Last) method, we obtain
$\text{Area}=40x^{2}+40x+200x+200$
Combining like terms, we have
$\text{Area}=40x^{2}+240x+200$
The polynomial that represents the area is $40x^{2}+240x+200$
(b) Given: $\text{width}=4x+20=160$
$\implies 4x=160-20=140$
$\implies x=\frac{140}{4}=35$
$\text{Area}=40x^{2}+240x+200$
$=40(35)^{2}+240(35)+200$
$=57600$
The area of the football field is $57600\,ft^{2}$
