a² - b² = (a - b)(a + b)
(a - b)² = a² - 2ab + b²
a^m*a^n = a^(m+n)
a^m / a ^n = a^(m - n)
(a^m)^n = a^(mn)
a) 115² - 115*110 + 55² = 115² - 2*55*115 + 55² = (115 - 55)² = 60²
105² - 135² + 15² - 45² = 105² - 45² + 15² - 135² = (105 - 45)(105 + 45) + (15 - 135)(15 + 135) = 60*150 - 120*150 = 150*(60 - 120) = -60*150
-60*150/60² = - 150/60 = -15/6 = -5/2 = -2 1/2 = - 2.5
б) 3¹⁰ - 5*3⁸ - 3⁷ = 3⁷*(3³ - 5*3 - 1) = 3⁷*(27 - 15 - 1) = 11*3⁷
2*9⁴ + 3⁷ - 10*9³ = 2*3⁸ + 3⁷ - 10*3⁶ = 3⁶*(2*3² + 3 - 10) = 3⁶*(18 + 3 - 10) = 11*3⁶
11*3⁷ / (11 *3⁶) = 3
