Fantastic four

Algebra Level 3

f(a+b)=f(a)+f(b)+4ab\large f(a+b)=f(a)+f(b)+4ab

The functional equation above is true for all real numbers aa and bb. Find the value of f(4)f\left( 4 \right), given that f(4)=40f\left( -4 \right) =40.

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