Functions, anyone?

Algebra Level 4

\(f:\mathbb{R} \rightarrow \mathbb{R} \)

\[\displaystyle(x-y)\times f(x+y)-(x+y)\times f(x-y)=4xy(x^2-y^2)\]

If \(\displaystyle f(1)=2\), find \(\displaystyle f(32)\).

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