2. Выполнить действия: 1) 21x⁵y⁶ ⋅ 2y³; 2) 3a⁴b⁵ ⋅ 6a²b; 3) (4a⁶ - b) ⋅ ab; 4) 2xy³(x + y); 5) 27a³b⁸ : (3ab²); 6) (a-3b)(3b + a).

1) 21x⁵y⁶ ⋅ 2y³:

21x⁵y⁶ ⋅ 2y³ = (21 * 2) * x⁵ * (y⁶ * y³) = 42x⁵y^(6+3) = 42x⁵y⁹.

Ответ: 42x⁵y⁹.

2) 3a⁴b⁵ ⋅ 6a²b:

3a⁴b⁵ ⋅ 6a²b = (3 * 6) * (a⁴ * a²) * (b⁵ * b) = 18 * a^(4+2) * b^(5+1) = 18a⁶b⁶.

Ответ: 18a⁶b⁶.

3) (4a⁶ - b) ⋅ ab:

(4a⁶ - b) ⋅ ab = 4a⁶ ⋅ ab - b ⋅ ab = 4a^(6+1)b - ab² = 4a⁷b - ab².

Ответ: 4a⁷b - ab².

4) 2xy³(x + y):

2xy³(x + y) = 2xy³ ⋅ x + 2xy³ ⋅ y = 2x²y³ + 2xy⁴.

Ответ: 2x²y³ + 2xy⁴.

5) 27a³b⁸ : (3ab²):

27a³b⁸ : (3ab²) = (27/3) * (a³/a) * (b⁸/b²) = 9 * a^(3-1) * b^(8-2) = 9a²b⁶.

Ответ: 9a²b⁶.

6) (a - 3b)(3b + a):

(a - 3b)(3b + a) = a(3b + a) - 3b(3b + a) = 3ab + a² - 9b² - 3ab = a² - 9b².

Ответ: a² - 9b².