Answer
(a) $x^{2}+100x+2500$
(b) $\text{Area}=4225\text{ sq. ft}$
$\text{Area of the extension}=1725\text{ sq. ft}$
Work Step by Step
(a) $(x+50)^{2}=x^{2}+50^{2}+2(x)(50)$
$=x^{2}+100x+2500$
(b) $\text{Area}=x^{2}+100x+2500$
When $x=15$,
$\text{Area}=(15)^{2}+100(15)+2500$
$=4225\text{ sq. ft}$
$\text{Area of the extension}=\text{Area of the house now}-\text{Area of the house before}$
$=4225-50^{2}=1725\text{ sq. ft}$
