Разложите на множители: 1) m³ + 27n³; 2) x³ – 64xy²; 3) -3a² + 18a – 27; 4) 2ab + 10b – 2a – 10; 5) a⁴– 16.

1) $$m^3 + 27n^3 = m^3 + (3n)^3 = (m + 3n)(m^2 - 3mn + 9n^2)$$

2) $$x^3 - 64xy^2 = x(x^2 - 64y^2) = x(x - 8y)(x + 8y)$$

3) $$-3a^2 + 18a - 27 = -3(a^2 - 6a + 9) = -3(a - 3)^2$$

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

5) $$a^4 - 16 = (a^2 - 4)(a^2 + 4) = (a - 2)(a + 2)(a^2 + 4)$$

Ответ:

1. $$(m + 3n)(m^2 - 3mn + 9n^2)$$
2. $$x(x - 8y)(x + 8y)$$
3. $$-3(a - 3)^2$$
4. $$2(b - 1)(a + 5)$$
5. $$(a - 2)(a + 2)(a^2 + 4)$$