Ф.И. Вариант. Выполните умножение и преобразуйте в многочлен стандартного вида: 1. (t - 8)(t + 4) 2. (15u - 4)(u + 1) 3. (p³ - 2)(p² + 1) 4. (12 - 5w)(3w - 2) 5. (2,2c + 4)(5c - 1) 6. (4 - d)(d² - 3d + 6)

Решение:

1. \( (t - 8)(t + 4) = t^2 + 4t - 8t - 32 = t^2 - 4t - 32 \)
2. \( (15u - 4)(u + 1) = 15u^2 + 15u - 4u - 4 = 15u^2 + 11u - 4 \)
3. \( (p^3 - 2)(p^2 + 1) = p^3 \cdot p^2 + p^3 \cdot 1 - 2 \cdot p^2 - 2 \cdot 1 = p^5 + p^3 - 2p^2 - 2 \)
4. \( (12 - 5w)(3w - 2) = 12 \cdot 3w - 12 \cdot 2 - 5w \cdot 3w + 5w \cdot 2 = 36w - 24 - 15w^2 + 10w = -15w^2 + 46w - 24 \)
5. \( (2.2c + 4)(5c - 1) = 2.2c \cdot 5c - 2.2c \cdot 1 + 4 \cdot 5c - 4 \cdot 1 = 11c^2 - 2.2c + 20c - 4 = 11c^2 + 17.8c - 4 \)
6. \( (4 - d)(d^2 - 3d + 6) = 4 \cdot d^2 - 4 \cdot 3d + 4 \cdot 6 - d \cdot d^2 + d \cdot 3d - d \cdot 6 = 4d^2 - 12d + 24 - d^3 + 3d^2 - 6d = -d^3 + (4d^2 + 3d^2) + (-12d - 6d) + 24 = -d^3 + 7d^2 - 18d + 24 \)

Ответ: 1. \( t^2 - 4t - 32 \); 2. \( 15u^2 + 11u - 4 \); 3. \( p^5 + p^3 - 2p^2 - 2 \); 4. \( -15w^2 + 46w - 24 \); 5. \( 11c^2 + 17.8c - 4 \); 6. \( -d^3 + 7d^2 - 18d + 24 \).