$$\eqalign{ & {7^{n + 2}} - {5^{n + 2}} + {5^n} + {7^n} = {7^{n + 2}} + {7^n} + {5^n} - {5^{n + 2}} = {7^n}\left( {{7^2} + 1} \right) - {5^n}\left( {{5^2} - 1} \right) = \cr & {7^n} \cdot 50 - {5^n} \cdot 2 \cdot 12 = {7^n} \cdot 50 - {5^{n - 2}} \cdot {5^2} \cdot 2 \cdot 12 = 50 \cdot \left( {{7^n} - 12 \cdot {5^{n - 2}}} \right) \cr} $$