Упростите выражение: 1) (5x² + 8x-7) - (2x2 – 2x – 12); 2) (2x-3)+(-2x2 – 5x – 18); 3) (6a² - 3a + 11) - (-3a - a³ + 7); 4) (14ab-9a² - 36²) - (-3a² + 5ab – 4b²); 5) (7xy² - 15xy + 3x²y) + (30xy - 8x²y); 6) (3/5 m³n²-1/4 mn²) - (5/8 n²m + 7/10 m³n²).

Решим по порядку:

1) \[ (5x^2 + 8x - 7) - (2x^2 - 2x - 12) = 5x^2 + 8x - 7 - 2x^2 + 2x + 12 = (5x^2 - 2x^2) + (8x + 2x) + (-7 + 12) = 3x^2 + 10x + 5 \] 2) \[ (2x - 3) + (-2x^2 - 5x - 18) = 2x - 3 - 2x^2 - 5x - 18 = -2x^2 + (2x - 5x) + (-3 - 18) = -2x^2 - 3x - 21 \] 3) \[ (6a^2 - 3a + 11) - (-3a - a^3 + 7) = 6a^2 - 3a + 11 + 3a + a^3 - 7 = a^3 + 6a^2 + (-3a + 3a) + (11 - 7) = a^3 + 6a^2 + 4 \] 4) \[ (14ab - 9a^2 - 3b^2) - (-3a^2 + 5ab - 4b^2) = 14ab - 9a^2 - 3b^2 + 3a^2 - 5ab + 4b^2 = (-9a^2 + 3a^2) + (14ab - 5ab) + (-3b^2 + 4b^2) = -6a^2 + 9ab + b^2 \] 5) \[ (7xy^2 - 15xy + 3x^2y) + (30xy - 8x^2y) = 7xy^2 - 15xy + 3x^2y + 30xy - 8x^2y = 7xy^2 + (-15xy + 30xy) + (3x^2y - 8x^2y) = 7xy^2 + 15xy - 5x^2y \] 6) \[ (\frac{3}{5} m^3n^2 - \frac{1}{4} mn^2) - (\frac{5}{8} n^2m + \frac{7}{10} m^3n^2) = \frac{3}{5} m^3n^2 - \frac{1}{4} mn^2 - \frac{5}{8} n^2m - \frac{7}{10} m^3n^2 = (\frac{3}{5} m^3n^2 - \frac{7}{10} m^3n^2) + (- \frac{1}{4} mn^2 - \frac{5}{8} mn^2) = (\frac{6}{10} m^3n^2 - \frac{7}{10} m^3n^2) + (- \frac{2}{8} mn^2 - \frac{5}{8} mn^2) = -\frac{1}{10} m^3n^2 - \frac{7}{8} mn^2 \]

Ответ: 1) 3x² + 10x + 5; 2) -2x² - 3x - 21; 3) a³ + 6a² + 4; 4) -6a² + 9ab + b²; 5) 7xy² + 15xy - 5x²y; 6) -1/10 m³n² - 7/8 mn²