(a^6-b^6)=(a³-b³)(a³+b³)=(a-b)(a²+ab+b²)(a+b)(a²-ab+b²)
29
1)(59³-41³)/18 +59*41=(59-41)(59²+59*41+41²)/18 +59*41=
=18(59²+59*41+41²)/18 +59*41=59²+2*59*41+41²)=(59+41)²=10000
2)[(97³+83³)/180 -97*83]:(35²-28²)=[(97+83)(97²-97*83+83²)/180-97*83]:(35-28)(35+28)=(97²-97*83+83²-97*83:7*63=(97-83)²:7*63=14²:7*63=196/441=4/9
3)(36,5²-27,5²):[(57³+33³)/90 -57*33]=(36,5-27,5)(36,5+27,5):[(57+33)(57²-57*33+33²)/90 -57*33]=9*64:(57²-57*33+33²-57*33)=9*64:(57-33)²=
=9*64/24²=576/576=1
4)(77³-69³)/(70²-62²) -(77³+41³)/(125²-49)=(77-69)(77²+77*69+69²)/(70-62)(70+62) -
-(77+41)(77²-77*41+41²)/(125-7)(125+7)=8*(77²+77*69+69²)/8*132-
-118(77²-77*41+41²)/118*132=(77²+77*69+69²)/132-(77²-77*41+41²)/132=
=77²+77*69+69²-77²+77*41-41²=(69²-41²)+77(69+41)=(69+41)(69-41)+77(69+41)=
=(69+41)(69-41+77)=110*105=11550