Answer
(a) $4x^{2}+84x+440$
(b) $840 \text{ in}^{2}$
Work Step by Step
(a) $\text{Area}=\text{length}\times\text{breadth}$
$=(x+20+x)(x+22+x)$
Combining like terms, we have
$\text{Area}=(2x+20)(2x+22)$
Using FOIL (First Outer Inner Last) method, we get
$\text{Area}=4x^{2}+44x+40x+440$
Combining like terms, we obtain
$\text{Area}=4x^{2}+84x+440$
The polynomial that represents the combined area is $4x^{2}+84x+440$.
(b) $\text{Width of the frame}=x=4$
$\implies \text{Area}=4(4)^{2}+84(4)+440=840$
The combined area is $840 \text{ in}^{2}$.
