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Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(p+1\right)^{3}.
p^{3}-\left(p^{3}+3p^{2}+3p+1\right)
To find the opposite of p^{3}+3p^{2}+3p+1, find the opposite of each term.
p^{3}-p^{3}-3p^{2}-3p-1
Combine p^{3} and -p^{3} to get 0.
-3p^{2}-3p-1
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