A³+b³=(a+b)(a²-ab+b²)
2) (x³+1)/(x²-x+1) -1 =(x³+x)/(x²+1)
(x³+1)/(x²-x+1)-1=(x+1)·(x²-x+1)/(x²-x+1)-1=x (x³+x)/(x²+1)=x(x²+1)/(x²+1)=x
x=x
3) a³+a²+3a+27=(a³+27)+(a²+3a+27)=(a+3)(a²+3a+27)+(a²+3a+27)=(a²+3a+27)(a+3+1)=(a²+3a+27)(a+4)
4) (3·5⁶-81)/33=3(5⁶-3³)/33=(5²-3)(5⁴+5²·3+3²)/11=(25-3)(625+25+9)/11=22·(659)/11=2·659=1318