07 Выполните умножение: a) 3x(x²-2x + 3); б)-4a(a² - 3ab + 7b); в) (2y³-6y² +12) (-1,5y³); г) 0,6a²b(3ab² - 8ab + 11a³b³); д) \( \frac{1}{3} mn (\frac{4}{3} m^2 - \frac{3}{2} mn^2 - \frac{5}{6} n^4) \); e) -2c³d⁴ (8c²-c³d + 4d³).

Решение:

1. a) \( 3x(x^2 - 2x + 3) = 3x \cdot x^2 - 3x \cdot 2x + 3x \cdot 3 = 3x^3 - 6x^2 + 9x \).
2. б) \( -4a(a^2 - 3ab + 7b) = -4a \cdot a^2 - (-4a) \cdot 3ab - 4a \cdot 7b = -4a^3 + 12a^2b - 28ab \).
3. в) \( (2y^3 - 6y^2 + 12)(-1.5y^3) = 2y^3 \cdot (-1.5y^3) - 6y^2 \cdot (-1.5y^3) + 12 \cdot (-1.5y^3) = -3y^6 + 9y^5 - 18y^3 \).
4. г) \( 0.6a^2b(3ab^2 - 8ab + 11a^3b^3) = 0.6a^2b \cdot 3ab^2 + 0.6a^2b \cdot (-8ab) + 0.6a^2b \cdot 11a^3b^3 = 1.8a^3b^3 - 4.8a^3b^2 + 6.6a^5b^4 \).
5. д) \( \frac{1}{3} mn (\frac{4}{3} m^2 - \frac{3}{2} mn^2 - \frac{5}{6} n^4) = \frac{1}{3} mn \cdot \frac{4}{3} m^2 - \frac{1}{3} mn \cdot \frac{3}{2} mn^2 - \frac{1}{3} mn \cdot \frac{5}{6} n^4 = \frac{4}{9} m^3n - \frac{1}{2} m^2n^3 - \frac{5}{18} mn^5 \).
6. е) \( -2c^3d^4 (8c^2 - c^3d + 4d^3) = -2c^3d^4 \cdot 8c^2 - (-2c^3d^4) \cdot c^3d - 2c^3d^4 \cdot 4d^3 = -16c^5d^4 + 2c^6d^5 - 8c^3d^7 \).