Răspuns:
[tex]\bf A=\green{2^{2n+2} \cdot 5^{2n+2}}\cdot 3- 2^{2n+3}\cdot 5^{2n+2}[/tex]
[tex]\bf A= 2^{2n+2} \cdot 5^{2n+2}\cdot\Big[ 2^{2n+2-(2n+2)} \cdot 5^{2n+2-(2n+2)}\cdot 3 -2^{2n+3-(2n+2)} \cdot 5^{2n+2-(2n+2)}\Big][/tex]
[tex]\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot\Big[2^{2n+2-2n-2} \cdot 5^{2n+2-2n-2}\cdot3 -2^{2n+3-2n-2} \cdot 5^{2n+2-2n-2}\Big][/tex]
[tex]\bf A=2^{2n+2} \cdot5^{2n+2}\cdot\Big[2^{0} \cdot 5^{0}\cdot3 -2^{1} \cdot 5^{0}\Big][/tex]
[tex]\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot\big(1 \cdot1\cdot3 -2 \cdot 1\big)[/tex]
[tex]\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot\big(3 -2\big)[/tex]
[tex]\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot1[/tex]
[tex]\bf A=2^{2\cdot(n+1)} \cdot 5^{2\cdot(n+1)}[/tex]
[tex]\bf A=\big(2 \cdot 5\big)^{2\cdot(n+1)}[/tex]
[tex]\bf A=\Big[\big(2 \cdot5\big)^{n+1}\Big]^{2}[/tex]
[tex]\red{\boxed{\bf A=\Big(10^{n+1}\Big)^{2}\implies patrat ~perfect~}}[/tex]
