Упростите выражение: a) (6x² - 7x + 4) - (4x² - 4x + 18); б) (3x + 9) + (-x² - 15x - 40); в) (10a² - 6a + 5) - (-11a + a³ + 6); г) (13xy - 11x² + 10y²) - (-15x² + 10xy - 15y²); д) (14ab² - 17ab + 5a²b) + (20ab - 14a²b); e) (7/8 x³y² - 5/6 xy²) - (-7/12 xy² + 5/12 x³y²).

Решение:

1. \( (6x^2 - 7x + 4) - (4x^2 - 4x + 18) = 6x^2 - 7x + 4 - 4x^2 + 4x - 18 = (6x^2 - 4x^2) + (-7x + 4x) + (4 - 18) = 2x^2 - 3x - 14 \)
2. \( (3x + 9) + (-x^2 - 15x - 40) = 3x + 9 - x^2 - 15x - 40 = -x^2 + (3x - 15x) + (9 - 40) = -x^2 - 12x - 31 \)
3. \( (10a^2 - 6a + 5) - (-11a + a^3 + 6) = 10a^2 - 6a + 5 + 11a - a^3 - 6 = -a^3 + 10a^2 + (-6a + 11a) + (5 - 6) = -a^3 + 10a^2 + 5a - 1 \)
4. \( (13xy - 11x^2 + 10y^2) - (-15x^2 + 10xy - 15y^2) = 13xy - 11x^2 + 10y^2 + 15x^2 - 10xy + 15y^2 = (-11x^2 + 15x^2) + (13xy - 10xy) + (10y^2 + 15y^2) = 4x^2 + 3xy + 25y^2 \)
5. \( (14ab^2 - 17ab + 5a^2b) + (20ab - 14a^2b) = 14ab^2 - 17ab + 5a^2b + 20ab - 14a^2b = 14ab^2 + (-17ab + 20ab) + (5a^2b - 14a^2b) = 14ab^2 + 3ab - 9a^2b \)
6. \( (\frac{7}{8} x^3y^2 - \frac{5}{6} xy^2) - (-\frac{7}{12} xy^2 + \frac{5}{12} x^3y^2) = \frac{7}{8} x^3y^2 - \frac{5}{6} xy^2 + \frac{7}{12} xy^2 - \frac{5}{12} x^3y^2 = (\frac{7}{8} x^3y^2 - \frac{5}{12} x^3y^2) + (-\frac{5}{6} xy^2 + \frac{7}{12} xy^2) \)
7. \( = (\frac{21}{24} x^3y^2 - \frac{10}{24} x^3y^2) + (-\frac{10}{12} xy^2 + \frac{7}{12} xy^2) = \frac{11}{24} x^3y^2 - \frac{3}{12} xy^2 = \frac{11}{24} x^3y^2 - \frac{1}{4} xy^2 \)

Ответ: а) 2x² - 3x - 14; б) -x² - 12x - 31; в) -a³ + 10a² + 5a - 1; г) 4x² + 3xy + 25y²; д) 14ab² + 3ab - 9a²b; е) \(\frac{11}{24} x^3y^2 - \frac{1}{4} xy^2\).