1. 3a³-81b³=3*(a³-27b³)=3*(a³-(3b)³)=3*(a-3b)*(a²+3ab+(3b)²)=
=(3a-9b)*(a²+3ab+(3b)²).
2. 18b²a+6a²b+2a³=2a*(9b²+3ab+a²)=2a*(a²+3ab+(3b)²).
3. (3a-9b)*(a²+3ab+(3b)²)/(2a*(a²+3ab+(3b)²))=(3a-9b)/(2a).
4. 81a²b-54ab²+9b³=9b*(9a²-6ab+b²)=9b*((3a)²-6ab+b²).
5. 2ab²-12ba²+18a³=2a*(b²-6ab+9a²)=2a*((3a)²-6ab+b²).
6. 9b*((3a)²-6ab+b²)/(2a*((3a)²-6ab+b²))=9b/(2a).
7. (3a-9b)/(2a)+9b/(2a)=(3a-9b+9b)/(2a)=3a/(2a)=3/2=1,5.