1)
а) 8m³+0.064p⁶=(2m)³+(0.4p²)³=(2m+0.4p²)(4m²-0.8mp²+0.16p⁴)
б) -27х³+0,008у⁹=(0,2у³)³-(3х)³=(0,2у³-3х)(0,04у⁶+0,6ху³+9х²)
2)
а) (2х-1)²-4(х-2)(х+2)=0
4х²-4х+1-4(х²-4)=0
4х²-4х+1-4х²+16=0
-4х=-17
х=-17 : (-4)
х=4,25
Ответ: 4,25
б) 1 х² = 0,81
9
х² - 0,81 =0
9
(х-0,9)(х+0,9)=0
3 3
х - 0,9 =0 х+0,9=0
3 3
х =0,9 х=-0,9
3 3
х=0,9*3 х=-0,9*3
х=2,7 х=-2,7
Ответ: -2,7; 2,7.
3)
а) 64х² - (х-1)²=(8х-(х-1))(8х+(х-1))=(8х-х+1)(8х+х-1)=(7х+1)(9х-1)
б) -а⁴+81=81-а⁴=(9-а²)(9+а²)=(3-а)(3+а)(9+а²)
4)
а) (-6а-2в)(6а-2в)=-(6а+2в)(6а-2в)=-(36а²-4в²)=4в²-36а²
б) (5m+0.2)(0.2-5m)=(0.2+5m)(0.2-5m)=(0.2)²-(5m)²=0.04-25m²