Answer:
[tex]-25x^{2} (\pi -9)[/tex]
Step-by-step explanation:
The area of the metal frame is equal to the area of the square minus the area of the circle.
The area of the square is the side length squared:
[tex](15x)^{2}[/tex]
[tex]=225x^{2}[/tex]
The area of the circle is [tex]\pi r^{2}[/tex], with [tex]r[/tex] being the radius:
[tex]\pi (5x)^{2}[/tex]
[tex]=\pi *25x^{2}[/tex]
[tex]=25\pi x^{2}[/tex]
Now find the area of the metal frame:
[tex]225x^{2} -25\pi x^{2}[/tex]
[tex]25x^{2} (9-\pi )[/tex] Factor out the GCF, [tex]25x^{2}[/tex]
[tex]-25x^{2} (\pi -9)[/tex] Factor out a [tex]-1[/tex]
