I.
1) 18у⁵-12ху²+9у³= 3у²·(6у³-4х+3у)
2) - 14аb³с²-21a²bc²-28a³b²c= -7abc·(2b²c+3ac+4a²b)
II.
1) a(3x-2y)+b(3x-2y) = (3x-2y)·(a+b)
2) (x+3)(2y-1)-(x+3)(3y+2)= (x+3)·(2y-1-3y-2)=(x+3)·(-y-3) = - (x+3)·(y+3)
III.
1) 3x-x²=0
x· (3-x) = 0
x₁ = 0;
3-x = 0 => x₂ = 3
ответ: {0; 3}
2) y²+5y=0
y·(у+5) = 0
у₁ = 0
у+5=0 => y₂ = -5
ответ: {0; -5}
IV.
27³+3⁷ = (3³)³ + 3⁷ = 3⁹ + 3⁷ = 3⁷· (3² + 1) = 3⁷· (9+1) = 3⁷ · 10
Понятие "кратно 10" означает "деление на 10 нацело"
(3⁷·10) : 10 = 3⁷ Доказано!
Объяснение:
5/4 и 3/2 = (3 * 2) /(2 * 2) = 6/4; б) 2/3 = (2 * 5)/(3 * 5) = 10/15 и 2/15 в) 7/15 = (7 * 3)/(15 * 3) = 21/45 и 5/9 = (5 * 5)/(9 * 5) = 25/45; г) 1/6 = (1 * 5)/(6 * 5) = 6/30 и 3/10 = (3 * 3)/(10 * 3) = 9/30; д) 1/3 = (1 * 6)/(3 * 6) = 6/18 и 5/18 е) 5/8 = (5 * 3)/(8 * 3) = 15/24 и 2/3 = (2 * 8)/(3 * 8) = 16/24; ж) 1/2 = (1 * 15)/(2 * 15) = 15/30 и 2/15 = (2 * 2)/(15 * 2) = 4/30; з) 5/12 = (5 * 5)/(12 * 5) = 25/60 и 7/15 = (7 * 2)/(15 * 2) = 14/30; и) 3/10 = (3 * 10)/(10 * 10) = 30/100 и 33/100.
