1) 1) a) 3ab² - 3ac² = 3a (b² - c²) = 3a (b - c)(b + c) ; b) 14 p² - 1 ; v) - 5k² + 5 = 5 (1 - k)(1 + k); g) 162ay² - 2a = 2a(81y² - 1) = 2a (9y - 1)(9y + 1); d) 100c⁴ - 81c⁴ = 19c⁴; e) 32x²y² - 2x = 2x (16xy² - 1); 2) a) 12x² + 12xy + 3y² = 3 (4x² + 4xy + y²) = 3 (2x + y)²; b) ab² - 2ab + a = a (b² - 2b + 1) = a (b - 1)²; v) 27x² + 3xy² - 18x²y = 3x (9x + y² - 6xy); g) -100x²y² + 20xy - 1 = - (10xy - 1)²; 3) a) a³ - 4a² - 2a + 8 = (a³ - 2a) - (4a² - 8) = a (a² - 2) - 4(a² - 2) = (a² - 2) (a - 4); b) a⁸ - a⁴ + a² - 1 = a⁴ (a⁴ - 1) + (a²- 1) = a⁴(a² - 1)(a² + 1) + (a² - 1) = (a² - 1) ( a⁴ (a² + 1) + 1) =(a² - 1) ( a⁶ + a⁴ +1) ; v) 9x² - 12x + 4 - y² = (3x - 2)² - y² = (3x - 2 - y) (3x - 2 + y); g) c² - x² - 2xy - y² = c² - (x + y)² = (c - x - y) (c +x +y); 5) a) (n + 6 + n - 6) (n + 6 - n + 6) = 2n · 12 = 24n ⇒ делится на 24; b) (3n + 1 + n - 1) (3n + 1 - n + 1) = 4n · 2(n+ 1) = 8n · (n + 1) ⇒ делится на 8;