Giải thích các bước giải:
Ta có :
$3^{n+2}$ - $2^{n+2}$ + $3^{n}$ - $2^{n}$ = $3^{n}$ . $3^{2}$ - $2^{n}$ . $2^{2}$ + $3^{n}$ - $2^{n}$
= $3^{n}$ . 9 - $2^{n}$ . 4 + $3^{n}$ - $2^{n}$ = $3^{n}$ . ( 9 + 1 ) - $2^{n}$ . ( 4 + 1 )
= $3^{n}$ . 10 - $2^{n}$ . 5 = $3^{n}$ . 10 - $2^{n-1}$ . 2 .5 = $3^{n}$ . 10 - $2^{n-1}$ . 10
= 10 . ( $3^{n}$ - $2^{n-1}$ ) ⋮ 10
⇒ $3^{n+2}$ - $2^{n+2}$ + $3^{n}$ - $2^{n}$ ⋮ 10 ( ĐPCM )