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| == Problem ==
| | #redirect [[2006 AMC 12A Problems/Problem 2]] |
| Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>?
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| <math> \mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math>
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| == Solution ==
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| Plugging our values into the defined [[operation]], we have
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| <center><math>\displaystyle h\otimes h = h^3-h</math></center>
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| Plugging in the [[function]] once more, we have
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| <center><math>\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h</math></center>
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| which is choice <math>(C)</math>.
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| == See also ==
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| {{AMC10 box|year=2006|ab=A|num-b=1|num-a=3}}
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| [[Category:Introductory Algebra Problems]]
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