[tex] {4}^{n} \times {3}^{n + 1} + {12}^{n + 1} - {6}^{n} \times {2}^{n + 1} [/tex]
[tex] = {( {2}^{2} )}^{n} \times {3}^{n + 1} + {(4 \times 3)}^{n + 1} - {(2 \times 3)}^{n} \times {2}^{n + 1} [/tex]
[tex]= {2}^{2n} \times {3}^{n + 1} + {4}^{n + 1} \times {3}^{n + 1} - {2}^{n} \times {3}^{n} \times {2}^{n + 1} [/tex]
[tex] = {2}^{2n} \times {3}^{n + 1} + {2}^{2n + 2} \times {3}^{n + 1} - {2}^{2n + 1} \times {3}^{n} [/tex]
[tex] = {2}^{2n} \times {3}^{n} (3 + {2}^{2} \times 3 - 2)[/tex]
[tex] = {2}^{2n} \times {3}^{n} (3 + 4 \times 3 - 2)[/tex]
[tex] = {2}^{2n} \times {3}^{n} (3 + 12 - 2)[/tex]
[tex] = {2}^{2n} \times {3}^{n} (15 - 2)[/tex]
[tex] = {2}^{2n} \times {3}^{n} \times 13\:\:\vdots\:\:13[/tex]
