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SMO 2015 Open Round 1 Question 16

SMO · SMO 2015 Open Round 1

Question 16

Let $f:\mathbb R\to\mathbb R$ be a function such that, for any $x,y\in\mathbb R$, $$(x-y)f(x+y)-(x+y)f(x-y)=(6x^2y+2y^3)(x^2-y^2).$$ Suppose $f(1)=-999$. Determine the value of $f(10)$.