Answer:
Area of a circle:
[tex]A=\pi r^2[/tex] (where r is the radius)
Area of largest (outer) circle:
[tex]\implies A=\pi (x+6)^2[/tex]
Area of inner circle:
[tex]\implies A=\pi x^2[/tex]
Area of space between the inner and outer circle:
[tex]\implies \pi (x+6)^2-\pi x^2[/tex]
[tex]\implies \pi [(x+6)^2- x^2][/tex]
[tex]\implies \pi (x^2+12x+36- x^2)[/tex]
[tex]\implies 12\pi x+36\pi[/tex]
Factored:
[tex]\implies 12\pi (x+3)[/tex]
