Дз 1. Разложите на множители: 1) m³ + 27n³; 4) 2ab + 10b – 2a - 10; 2) x³- 64xy²; 5) a4 - 16. 3)-3a² + 18 - 27; 2. Упростите выражение (2а- 1)(4a² + 2a + 1) и найдите 1 его значение при а = 2 3. Разложите на множители: 1) x2y² + x - y; 2) 4x24xy + y² - 9; 4. Решите уравнение: 1) 6x324x = 0; 3) ac4-c4-ac² + c²; 4) 4m² + 2mn - n². 3)x34x29x + 36 = 0.

1. m³ + 27n³ = m³ + (3n)³ = (m + 3n)(m² - 3mn + 9n²)

2. x³ - 64xy² = x(x² - 64y²) = x(x - 8y)(x + 8y)

3. -3a² + 18a - 27 = -3(a² - 6a + 9) = -3(a - 3)²

4. 2ab + 10b - 2a - 10 = 2b(a + 5) - 2(a + 5) = (a + 5)(2b - 2) = 2(a + 5)(b - 1)

5. a⁴ - 16 = (a²)² - 4² = (a² - 4)(a² + 4) = (a - 2)(a + 2)(a² + 4)

(2a - 1)(4a² + 2a + 1) = 8a³ + 4a² + 2a - 4a² - 2a - 1 = 8a³ - 1

При a = -1/2: 8(-1/2)³ - 1 = 8(-1/8) - 1 = -1 - 1 = -2

Ответ: -2

1. x² - y² + x - y = (x - y)(x + y) + (x - y) = (x - y)(x + y + 1)

2. 4x² - 4xy + y² - 9 = (2x - y)² - 3² = (2x - y - 3)(2x - y + 3)

3. ac⁴ - c⁴ - ac² + c² = c⁴(a - 1) - c²(a - 1) = (a - 1)(c⁴ - c²) = c²(a - 1)(c² - 1) = c²(a - 1)(c - 1)(c + 1)

4. 4 - m² + 2mn - n² = 4 - (m² - 2mn + n²) = 2² - (m - n)² = (2 - (m - n))(2 + (m - n)) = (2 - m + n)(2 + m - n)

1. 6x³ - 24x = 0

   6x(x² - 4) = 0

   6x(x - 2)(x + 2) = 0

   x = 0, x = 2, x = -2

2. x³ - 4x² - 9x + 36 = 0

   x²(x - 4) - 9(x - 4) = 0

   (x - 4)(x² - 9) = 0

   (x - 4)(x - 3)(x + 3) = 0

   x = 4, x = 3, x = -3