# Quite large

Algebra Level 4

Let $$f(x) = 9x+2$$ and $$g(x) = 25x+6$$. Find the sum of all possible constant terms of all functions that are compositions of the functions $$f$$ and $$g$$ in which $$f$$ and $$g$$ each appear exactly 4 times.

For example, a composition of $$f$$ and $$g$$ in which $$f$$ and $$g$$ each appear exactly 2 times could be $$f(f(g(g(x))))$$ or $$f(g(f(g(x))))$$.

Also note that the constant term of a function $$h$$ is equal to $$h(0)$$.

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