1)
1. 3x²y⁴ + 9xy³ = 3xy³(xy + 3)
2. x² - 7x - 8 = x² - 8x - 8 + x = x(x + 1) - 8(x + 1) = (x - 8)(x + 1)
3. 9x²y - y²b + 9x²b - yb² = 9x²(y + b) - yb(y + b) = (9x² - yb)(y + b)
4. x(x - 1) + (1 - x) = x² - x + 1 - x = x² - 2x + 1 = (x - 1)²
2)
64⁸ + 16¹¹ ··· 17
8¹⁶ + 4²² ··· 17
2⁴⁸ + 2⁴⁴ ··· 17
2⁴⁴(2⁴ + 1) ··· 17
2⁴⁴(16 + 1) ··· 17
2⁴⁴ * 17 ··· 17
Если один из множителей делится на 17, значит и число делится на 17
3)
139 * 15 + 18 * 139 + 15 * 261 + 18 * 261 =
15(139 + 261) + 18(139 + 261) =
(15 + 18)(139 + 261) =
33 * 400 = 13200
(2 3/8 : 3/4 - 24 7/9) : (7 1/8 - 157 4/5 : 24)
1) 2 3/8 : 3/4 = 19/8 * 4/3 = 19/6 = 3 1/6,
2) 3 1/6 - 24 7/9 = 19/6 - 223/9 = 57/18 - 446/18 = -389/18 = -21 11/18,
3) 157 4/5 : 24 = 789/5 * 1/24 = 263/40 = 6 3/40,
4) 7 1/8 - 6 3/40 = 57/8 - 263/40 = 285/40 - 263/40 = 22/40 = 11/20,
5) -21 11/18 : 11/20 = -389/18 * 20/11 = -3890/99 = -39 29/99