2. Запишите в виде многочлена: 1) 3ab(a²-2ab+b²) 2) -x²y(x²y²-x²-y²) 3) 2,5a²b(4a²-2ab+0,2b²) 4) (-2ax²+3ax-a²)(-a²x²) 5) (6,3x³y-3y²-0,7x)·10x²y² 6) -1,4p²q⁶(5p³q-1,5pq²-2q³) 7) \(\frac{1}{2}\)ab\(\frac{2}{3}a²-\frac{3}{4}ab+\frac{4}{5}b\) 8) -\(\frac{2}{5}\)a²y⁵\(5ay²-\frac{1}{2}a²y-\frac{5}{6}a³\)

Решение:

1. \( 3ab(a^2-2ab+b^2) = 3ab \cdot a^2 - 3ab \cdot 2ab + 3ab \cdot b^2 = 3a^3b - 6a^2b^2 + 3ab^3 \)
2. \( -x^2y(x^2y^2-x^2-y^2) = -x^2y \cdot x^2y^2 - x^2y \cdot (-x^2) - x^2y \cdot (-y^2) = -x^4y^3 + x^4y + x^2y^3 \)
3. \( 2,5a^2b(4a^2-2ab+0,2b^2) = 2,5a^2b \cdot 4a^2 - 2,5a^2b \cdot 2ab + 2,5a^2b \cdot 0,2b^2 = 10a^4b - 5a^3b^2 + 0,5a^2b^3 \)
4. \( (-2ax^2+3ax-a^2)(-a^2x^2) = -2ax^2 \cdot (-a^2x^2) + 3ax \cdot (-a^2x^2) - a^2 \cdot (-a^2x^2) = 2a^3x^4 - 3a^3x^3 + a^4x^2 \)
5. \( (6,3x^3y-3y^2-0,7x) \cdot 10x^2y^2 = 6,3x^3y \cdot 10x^2y^2 - 3y^2 \cdot 10x^2y^2 - 0,7x \cdot 10x^2y^2 = 63x^5y^3 - 30x^2y^4 - 7x^3y^2 \)
6. \( -1,4p^2q^6(5p^3q-1,5pq^2-2q^3) = -1,4p^2q^6 \cdot 5p^3q - 1,4p^2q^6 \cdot (-1,5pq^2) - 1,4p^2q^6 \cdot (-2q^3) = -7p^5q^7 + 2,1p^3q^8 + 2,8p^2q^9 \)
7. \( \frac{1}{2}ab(\frac{2}{3}a^2-\frac{3}{4}ab+\frac{4}{5}b) = \frac{1}{2}ab \cdot \frac{2}{3}a^2 - \frac{1}{2}ab \cdot \frac{3}{4}ab + \frac{1}{2}ab \cdot \frac{4}{5}b = \frac{1}{3}a^3b - \frac{3}{8}a^2b^2 + \frac{2}{5}ab^2 \)
8. \( -\frac{2}{5}a^2y^5(5ay^2-\frac{1}{2}a^2y-\frac{5}{6}a^3) = -\frac{2}{5}a^2y^5 \cdot 5ay^2 - \frac{2}{5}a^2y^5 \cdot (-\frac{1}{2}a^2y) - \frac{2}{5}a^2y^5 \cdot (-\frac{5}{6}a^3) = -2a^3y^7 + \frac{1}{5}a^4y^6 + \frac{1}{3}a^5y^5 \)

Ответ: 1) \( 3a^3b - 6a^2b^2 + 3ab^3 \); 2) \( -x^4y^3 + x^4y + x^2y^3 \); 3) \( 10a^4b - 5a^3b^2 + 0,5a^2b^3 \); 4) \( 2a^3x^4 - 3a^3x^3 + a^4x^2 \); 5) \( 63x^5y^3 - 30x^2y^4 - 7x^3y^2 \); 6) \( -7p^5q^7 + 2,1p^3q^8 + 2,8p^2q^9 \); 7) \( \frac{1}{3}a^3b - \frac{3}{8}a^2b^2 + \frac{2}{5}ab^2 \); 8) \( -2a^3y^7 + \frac{1}{5}a^4y^6 + \frac{1}{3}a^5y^5 \).