[tex]5^{2n+1}\times4^{3n+2}+10^{2n+1}\times2^{4n+1}=[/tex]
[tex]=5^{2n+1}\times(2^2)^{3n+2}+(5\times2)^{2n+1}\times2^{4n+1}=[/tex]
[tex]=5^{2n+1}\times2^{6n+4}+5^{2n+1}\times2^{2n+1}\times2^{4n+1}=[/tex]
[tex]=5^{2n+1}\times2^{6n+4}+5^{2n+1}\times2^{2n+1+4n+1}=[/tex]
[tex]=5^{2n+1}\times2^{6n+4}+5^{2n+1}\times2^{6n+2}=[/tex]
[tex]=5^{2n+1}\times2^{6n+2}\times(2^2+1)=[/tex]
[tex]=5^{2n+1}\times2^{6n+2}\times5=[/tex]
[tex]=5^{2n+2}\times2^{6n+2}=[/tex]
[tex]=5^{2(n+1)}\times2^{2(3n+1)}=[/tex]
[tex]=(5^{n+1}\times2^{3n+1})^2=[/tex]
[tex]=(5^{n+1}\times2^{n+1}\times2^{2n})^2=[/tex]
[tex]=((5\times2)^{n+1}\times4^n)^2=[/tex]
[tex]=(4^n\times10^{n+1})^2[/tex]
