Question

Розкладіть на множники:

Answer 1

$a^{n+4}-a^{n-5}=a^{n-5}\left ( a^{n+4-n+5}-1 \right )=a^{n-5}\left ( a^9 -1\right )=a^{n-5}(a-1)\left ( a^2+a+1 \right )\left ( a^6+a^3+1 \right )$

$b^{2n}+b^{3n}=b^{2n}\left ( 1+b^{3n-2n} \right )=b^{2n}\left ( 1+b \right )$

$3^{n+3}-5\cdot 3^{n+2}+2\cdot 3^n=3^n\left ( 3^{n+3-n}-5\cdot 3^{n+2-n}+2 \right )=3^n\left ( 27-45+2 \right )=-16\cdot 3^n$

$64^{n+2}-32^{n+2}+16^{n+2}=16^{n+2}\left ( -2^{n+2}+2^{2n+4}+1 \right )$