Question

what is the expression for the area of the shaded region in the diagram in factored form?

diagram:
(shaded) Large circle have diameter of 8x
(clear) small circle have diameter of 8y
___

my work:
Area of large circle - Area of small circle
Pi * 4^2 - pi * 4^2 = pi ( 2x+2y)(2x-2y)


my work correct?

Answer 1

pi*(4x)^2 - pi(4y)^2
= 16pi x^2 - 16pi y^2
= 16pi (x+y)(x-y)

Your mistake was in saying that

pi(4x)^2 = pi*4x^2
Bzzzzt

Parentheses are yur friends.