# 2006 AMC 12A Problems/Problem 2

The following problem is from both the 2006 AMC 12A #2 and 2006 AMC 10A #2, so both problems redirect to this page.

## 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

By the definition of $\otimes$, we have $h\otimes h=h^{3}-h$. Then $h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=h$. The answer is $\mathrm{(C)}$.

## Solution 2

Substitute $1$ for $h$. You get $1^3-(1^3-1)$ which is $1$. That is $h$, so the answer is $\mathrm{(C)}$. ~dragoon also aop is a god

## See also

 2006 AMC 12A (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 3 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions
 2006 AMC 10A (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 3 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions

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