356. Выполните умножение: 1) 3x(4x² -x); 2)-5a² (a²-6a-3); 3) (8b2-10b+2)⋅ 0,5b; 4) x³(x5-x²+7x-1); 5) -2c²d⁴(4c²c³d + 5d⁴); 6) (5m³n-8mn² - 2n)⋅ (-4m²n³).

Решение:

1. \[ 3x(4x^2 - x) = 3x \cdot 4x^2 - 3x \cdot x = 12x^3 - 3x^2 \]
2. \[ -5a^2(a^2 - 6a - 3) = -5a^2 \cdot a^2 - 5a^2 \cdot (-6a) - 5a^2 \cdot (-3) = -5a^4 + 30a^3 + 15a^2 \]
3. \[ (8b^2 - 10b + 2) \cdot 0.5b = 8b^2 \cdot 0.5b - 10b \cdot 0.5b + 2 \cdot 0.5b = 4b^3 - 5b^2 + b \]
4. \[ x^3(x^5 - x^2 + 7x - 1) = x^3 \cdot x^5 - x^3 \cdot x^2 + x^3 \cdot 7x - x^3 \cdot 1 = x^8 - x^5 + 7x^4 - x^3 \]
5. \[ -2c^2d^4(4c^2c^3d + 5d^4) = -2c^2d^4 \cdot 4c^2c^3d - 2c^2d^4 \cdot 5d^4 = -8c^7d^5 - 10c^2d^8 \]
6. \[ (5m^3n - 8mn^2 - 2n) \cdot (-4m^2n^3) = 5m^3n \cdot (-4m^2n^3) - 8mn^2 \cdot (-4m^2n^3) - 2n \cdot (-4m^2n^3) = -20m^5n^4 + 32m^3n^5 + 8m^2n^4 \]