Answer
(a) $10000-x^{2}$
(b) Area of the parking lot decreases.
$\text{Area before}=100^{2}$
$\text{Area after}=100^{2}-x^{2}$
The area decreases by $x^{2}$.
(c) $9559\text{ sq.ft}$
Work Step by Step
(a) Using sum and difference pattern, we have
$(100-x)(100+x)=100^{2}-x^{2}$
$=10000-x^{2}$
(b) Area of the parking lot decreases.
$\text{Area before}=100^{2}$
$\text{Area after}=100^{2}-x^{2}$
The area decreases by $x^{2}$.
(c) When $x=21$,
$\text{Area}=10000-(21)^{2}=9559\text{ sq.ft}$
