Answer
$25x^2(9-\pi)$
Work Step by Step
The area of the metal portion of the frame is the total area reduced by the area taken up by the mirror.
The total area inside the frame is
$l\times w=15x\times15x=225x^2$
The area of the circular mirror is
$\pi r^2=\pi(5x)^2=25\pi x^2$
The area of the metal portion of the frame is the total area reduced by the area taken up by the mirror.
$225x^2-25\pi x^2$
Find the greatest common factor of the terms. Find the prime factors of each term. Multiply the common factors to find the GCF.
$225x^2=\underline5\times\underline5\times9\times\underline x\times\underline x$
$25\pi x^2=\underline5\times\underline5\times\pi \times\underline x\times\underline x$
GCF$=5\times5\times x\times x=25x^2$
Factor the GCF out of each term. Use the factors that were not part of the GCF.
$225x^2-25\pi x^2=25x^2(9-\pi)$
