\(\begin{array}{l}a)\,{9^4} + {27^3} + {3^6} + {111^2}\\ = {\left( {{3^2}} \right)^4} + {\left( {{3^3}} \right)^3} + {3^6} + {\left( {3.37} \right)^2}\\ = {3^8} + {3^9} + {3^6} + {3^2}{.37^2}\\ = {3^6}\left( {{3^2} + {3^3} + 1} \right) + {3^2}{.37^2}\\ = {3^6}.37\,\, + {9.37^2}\\ = 37.\left( {{3^6} + 9.37} \right)\,\,\, \vdots \,\,\,37\end{array}\)
\(\begin{array}{l}b)\,\,{3^{n + 2}} - {2^{n + 2}} + {3^n} - {2^n}\\ = {3^2}{.3^n} - {2^2}{.2^n} + {3^n} - {2^n}\\ = ({9.3^n} + {3^n}) - \left( {{{4.2}^n} + {2^n}} \right)\\ = {3^n}.10 - {5.2^n}\\ = {3^n}.10 - {5.2.2^{n - 1}}\\ = {3^n}.10 - {10.2^{n - 1}}\\ = 10.\left( {{3^n} - {2^{n - 1}}} \right)\,\, \vdots \,\,10\end{array}\)