Неделя 1, Задание 3: Упростите выражение.

Решение:

1. \( (6x^2 - 7x + 4) - (4x^2 - 4x + 18) = 6x^2 - 7x + 4 - 4x^2 + 4x - 18 = 2x^2 - 3x - 14 \)
2. \( (3x + 9) + (-x^2 - 15x - 40) = 3x + 9 - x^2 - 15x - 40 = -x^2 - 12x - 31 \)
3. \( (10a^2 - 6a + 5) - (-11a + a^3 + 6) = 10a^2 - 6a + 5 + 11a - a^3 - 6 = -a^3 + 10a^2 + 5a - 1 \)
4. \( (13xy - 11x^2 + 10y^2) - (-15x^2 + 10xy - 15y^2) = 13xy - 11x^2 + 10y^2 + 15x^2 - 10xy + 15y^2 = 4x^2 + 3xy + 25y^2 \)
5. \( (14ab^2 - 17ab + 5a^2b) + (20ab - 14a^2b) = 14ab^2 - 17ab + 5a^2b + 20ab - 14a^2b = 14ab^2 + 3ab - 9a^2b \)
6. \( \left(\frac{7}{5}x^3y^2 - \frac{5}{6}x^2y^2\right) - \left(-\frac{7}{12}x^3y^2 + \frac{5}{12}x^3y^2\right) = \frac{7}{5}x^3y^2 - \frac{5}{6}x^2y^2 + \frac{7}{12}x^3y^2 - \frac{5}{12}x^3y^2 \) \( = \left(\frac{7}{5} + \frac{7}{12} - \frac{5}{12}\right)x^3y^2 - \frac{5}{6}x^2y^2 = \left(\frac{7}{5} + \frac{2}{12}\right)x^3y^2 - \frac{5}{6}x^2y^2 = \left(\frac{7}{5} + \frac{1}{6}\right)x^3y^2 - \frac{5}{6}x^2y^2 = \left(\frac{42+5}{30}\right)x^3y^2 - \frac{5}{6}x^2y^2 = \frac{47}{30}x^3y^2 - \frac{5}{6}x^2y^2 \)

Ответ: 1) \(2x^2 - 3x - 14\); 2) \(-x^2 - 12x - 31\); 3) \(-a^3 + 10a^2 + 5a - 1\); 4) \(4x^2 + 3xy + 25y^2\); 5) \(14ab^2 + 3ab - 9a^2b\); 6) \(\frac{47}{30}x^3y^2 - \frac{5}{6}x^2y^2\).