№ 41. Выполните умножение: а) - 0,2x (x⁴ - 1,6х³ + 2,3x)·x²; б) 2/3 ab(0,3a² - 1,2ab + 1)·a³; в) - 1/9 (0,5a²b² - ab + 0,9)·(-ab); г) -b³(-0,3a²b - 0,4ab + 1)· 1/6 ab²; д) 4x^y (3x - 2y^).

Решение:

1. а) \( -0.2x(x^4 - 1.6x^3 + 2.3x)x^2 = -0.2x^3(x^4 - 1.6x^3 + 2.3x) = -0.2x^7 + 0.32x^6 - 0.46x^4 \)
2. б) \( \frac{2}{3}ab(0.3a^2 - 1.2ab + 1)a^3 = \frac{2}{3}a^4b(0.3a^2 - 1.2ab + 1) = 0.2a^6b - 0.8a^5b^2 + \frac{2}{3}a^4b \)
3. в) \( -\frac{1}{9}(0.5a^2b^2 - ab + 0.9)(-ab) = -\frac{1}{9}(-0.5a^3b^3 + a^2b^2 - 0.9ab) = \frac{1}{18}a^3b^3 - \frac{1}{9}a^2b^2 + 0.1ab \)
4. г) \( -b^3(-0.3a^2b - 0.4ab + 1) \cdot \frac{1}{6}ab^2 = -\frac{1}{6}ab^5(-0.3a^2b - 0.4ab + 1) = 0.05a^3b^6 + \frac{0.4}{6}a^2b^6 - \frac{1}{6}ab^5 = 0.05a^3b^6 + \frac{2}{15}a^2b^6 - \frac{1}{6}ab^5 \)
5. д) \( 4x^y(3x - 2y) = 12x^{y+1} - 8x^y y \)