Question

2^n+1×3^n+2-6^n ajutor!​

Answer 1

Răspuns:

$17\cdot 6^n$

Explicație pas cu pas:

$2^{n+1}\cdot 3^{n+2}-6^n =$

$=2^{n+1}\cdot 3^{n+1+1}-6^n$

$=2^{n+1}\cdot 3^{n+1}\cdot 3-6^n$

$=(2\cdot 3)^{n+1}\cdot 3-6^n$

$=6^{n+1}\cdot 3-6^n$

$=6^{n}\cdot 6\cdot 3-6^n$

$=6^{n}\cdot 18-6^n$

$=6^{n}\cdot (18-1)$

$=6^{n}\cdot 17$

$=17\cdot 6^{n}$