5. Разложите на множители: Вариант I 1) 16x² - 49; 2) 9a² + 30ab + 25b²; 3) y³ + 18y² + 81y; 4) xy⁴ - 2y⁴ - xy + 2y Вариант II 1) 25y² - 4; 2) 36a² - 60ab + 25b²; 3) x³ - 8x² + 16x; 4) ab⁵ - b⁵ - ab³ + b³

Вариант I 1) \(16x^2 - 49 = (4x)^2 - 7^2 = (4x - 7)(4x + 7)\) 2) \(9a^2 + 30ab + 25b^2 = (3a)^2 + 2 * (3a) * (5b) + (5b)^2 = (3a + 5b)^2\) 3) \(y^3 + 18y^2 + 81y = y(y^2 + 18y + 81) = y(y + 9)^2\) 4) \(xy^4 - 2y^4 - xy + 2y = y^4(x-2) - y(x - 2) = y(x-2)(y^3 - 1) = y(x-2)(y-1)(y^2+y+1)\) Вариант II 1) \(25y^2 - 4 = (5y)^2 - 2^2 = (5y - 2)(5y + 2)\) 2) \(36a^2 - 60ab + 25b^2 = (6a)^2 - 2 * (6a) * (5b) + (5b)^2 = (6a - 5b)^2\) 3) \(x^3 - 8x^2 + 16x = x(x^2 - 8x + 16) = x(x - 4)^2\) 4) \(ab^5 - b^5 - ab^3 + b^3 = b^5(a - 1) - b^3(a - 1) = b^3(a - 1)(b^2 - 1) = b^3(a - 1)(b - 1)(b + 1)\)