If p + 1/p = 112, find the value of ( p - 112 )^15 + 1p^15 = ?

Answer: Option B

$$\begin{array}{rl}& p+\frac{1}{p}=112,{\left(p-112\right)}^{15}+\frac{1}{p^{15}}=?\\ & p-112=-\frac{1}{p}\\ & {\left(p-112\right)}^{15}+\frac{1}{p^{15}}\\ & ={\left(-\frac{1}{p}\right)}^{15}+\frac{1}{p^{15}}\\ & =-\frac{1}{p^{15}}+\frac{1}{p^{15}}\\ & =0\end{array}$$