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Which one of the following is equivalent to the expression ${(h+1)}^{3}+3$?

A

${h}^{2}-2h+3$

B

${{h}^{3}+3h}^{2}+3h+4$

C

${{h}^{3}-h}^{2}+4$

D

${h}^{2}+4h+4$

E

${h}^{3}-3{h}^{2}+4$

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