2006 AMC 10A Problems/Problem 2

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Problem

Define $x\otimes y=x^3-y$. What is $h\otimes (h\otimes h)$?

$\mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3$

Solution

Plugging our values in the function, we have

$h^3-h$

Plugging in the function once more, we have

$h^3-(h^3-h)=h, (C)$

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