Выполните умножение: 1. 5x(x-4) 2. -3a²(a+2) 3. 2mn(m-n²) 4. -4k(k²-k+1) 5. 7p²q(p-q) 6. -x²y³(xy-y²) 7. 6b(b²+3b-2) 8. -2uv²(u²-v) 9. 3a³b(ab²-a²) 10. -c²d²(c²d-cd²+1)

Решение:

1. \( 5x(x-4) = 5x \cdot x - 5x \cdot 4 = 5x^2 - 20x \)
2. \( -3a^2(a+2) = -3a^2 \cdot a - 3a^2 \cdot 2 = -3a^3 - 6a^2 \)
3. \( 2mn(m-n^2) = 2mn \cdot m - 2mn \cdot n^2 = 2m^2n - 2mn^3 \)
4. \( -4k(k^2-k+1) = -4k \cdot k^2 - (-4k) \cdot k + (-4k) \cdot 1 = -4k^3 + 4k^2 - 4k \)
5. \( 7p^2q(p-q) = 7p^2q \cdot p - 7p^2q \cdot q = 7p^3q - 7p^2q^2 \)
6. \( -x^2y^3(xy-y^2) = -x^2y^3 \cdot xy - (-x^2y^3) \cdot y^2 = -x^3y^4 + x^2y^5 \)
7. \( 6b(b^2+3b-2) = 6b \cdot b^2 + 6b \cdot 3b - 6b \cdot 2 = 6b^3 + 18b^2 - 12b \)
8. \( -2uv^2(u^2-v) = -2uv^2 \cdot u^2 - (-2uv^2) \cdot v = -2u^3v^2 + 2uv^3 \)
9. \( 3a^3b(ab^2-a^2) = 3a^3b \cdot ab^2 - 3a^3b \cdot a^2 = 3a^4b^3 - 3a^5b \)
10. \( -c^2d^2(c^2d-cd^2+1) = -c^2d^2 \cdot c^2d - (-c^2d^2) \cdot cd^2 + (-c^2d^2) \cdot 1 = -c^4d^3 + c^3d^4 - c^2d^2 \)

Ответ: 1. 5x² - 20x; 2. -3a³ - 6a²; 3. 2m²n - 2mn³; 4. -4k³ + 4k² - 4k; 5. 7p³q - 7p²q²; 6. -x³y⁴ + x²y⁵; 7. 6b³ + 18b² - 12b; 8. -2u³v² + 2uv³; 9. 3a⁴b³ - 3a⁵b; 10. -c⁴d³ + c³d⁴ - c²d².