Answer
For any values of x and y is the equation(x2 + y2)2 = (x2 – y2)2 + (2xy)2 is true
Solution
Consider the identities
(a + b)^2 = a2 + b2 +2ab ------(1)
(a - b)^2 = a2 + b2 -2ab ------(2)
from (1) and (2) we can write
(a + b)^2 = (a - b)^2 + 4ab
Here a=x2 and b=y2
(x2 + y2)2 = (x2)2 + (y2)2 +2x2y2
(x2 - y2)2 = (x2)2 + (y2)2 -2x2y2
Therefore
(x2 + y2)2 = (x2 – y2)2 + (2xy)2
For any values of x and y is the equation (x2 + y2)2 = (x2 – y2)2 + (2xy)2 is true