Answer
$25x^{2}(9-\pi)$.
Work Step by Step
$ A_{1}=\pi r^{2}\qquad$...area of a circle
$ A_{1}=\pi(5x)^{2}\qquad$...substitute 5x for r.
$A_{1}=25\pi x^{2}\qquad...$simplify.
$A_{2}=s^{2}\qquad...$area of a square.
$A_{2}=(15x)^{2}\qquad...$substitute 15x for s.
$A_{2}=225x^{2}\qquad...$simplify.
The area of the metal frame is $A_{2}-A_{1}$, or $225x^{2}-25\pi x^{2}$.
$225x^{2}-25\pi x^{2}\qquad...$find the GCF.
$225x^{2}=3\cdot 3\cdot(5\cdot 5)\cdot(x\cdot x)$
$-25\pi x^{2}=-1\cdot(5\cdot 5)\cdot\pi\cdot(x\cdot x)$
GCF=$(5\cdot 5)\cdot(x\cdot x)$, or $25x^{2}$.
$225x^{2}-25\pi x^{2}\qquad...$factor out the GCF
$=25x^{2}(9)-25x^{2}(\pi)\qquad...$apply the Distributive Property.
$=25x^{2}(9-\pi)$
The factored form of the area of the metal frame is $25x^{2}(9-\pi)$.
