Functions are awesome!!! -Part 3

Algebra Level 5

Find the number of functions such that \[f:RÔ×íR\] satisfying: \[f(x+y)f(x-y)=(f(x)+f(y))^{2}-4x^{2}f(y)\] where \(x,y\) belong to \(R\) for all real numbers.

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