A circular mirror is surrounded by a square metal frame. The radius of the mirror is 5x. The side length of the metal frame is 15x. What is the area of the metal frame? Write your answer in factored form.

To find the area of the metal frame, we need to subtract the area of the circular mirror from the area of the square frame.

The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. In this case, the radius of the mirror is given as 5x, so the area of the mirror is A_mirror = π(5x)^2.

The area of a square can be calculated using the formula A = s^2, where A is the area and s is the side length. In this case, the side length of the frame is given as 15x, so the area of the frame is A_frame = (15x)^2.

To find the area of the metal frame, we subtract the area of the mirror from the area of the frame:

A_metal frame = A_frame - A_mirror
= (15x)^2 - π(5x)^2

Now, let's factor out the common factors:

A_metal frame = x^2(15^2 - π5^2)

Simplifying further:

A_metal frame = x^2(225 - 25π)

So, the area of the metal frame, in factored form, is x^2(225 - 25π).