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Answer:
1. (12y² + 17y - 4) + (9y² - 13y + 3)
= (12y² + 9y²) + (17y - 13y) + (-4 + 3)
= 21y² + 4y - 1
2. (2x³ + 7x² + x) + (2x² - 4x - 12)
= 2x³ + (7x² + 2x²) + (x - 4x) - 12
= 2x³ + 9x² - 3x - 12
3. (-3m² + m) + (4m² + 6m)
= (-3m² + 4m²) + (m + 6m)
= m² + 7m
4. (7z³ + 4z - 1) + (2z² - 6z + 2)
= 7z³ + 2z² + (4z - 6z) + (-1 + 2)
= 7z³ + 2z² - 2z + 1
5. (3a² + 2a - 2) - (a² - 3a + 7)
= (3a² - a²) + (2a + 3a) + (-2 - 7)
= 2a² + 5a - 9
6. (5x² - 2x - 1) - (3x² - 5x + 7)
= (5x² - 3x²) + (-2x + 5x) + (-1 - 7)
= 2x² + 3x - 8
7. -(3z² + 4z) - (6z² - 2)
= (-3z² - 6z²) - 4z + 2
= -9z² - 4z + 2
8. (6x³ - 4x² + x - 9) - (3x² + 7x + 13)
= 6x³ + (-4x² - 3x²) + (x - 7x) + (-9 - 13)
= 6x³ - 7x² - 6x - 22
9. (2x² + 1) + (x² - 2x + 1)
= (2x² + x²) - 2x + (1 + 1)
= 3x² - 2x + 2
10. (-s² - 3) - (2s² + 10s)
= (-s² - 2s²) - 10s - 3
= -3s² - 10s - 3
11. (5 - 9a³) + (4a² + 6a - 3)
= -9a³ + 4a² + 6a + (5 - 3)
= -9a³ + 4a² + 6a + 2
12. (3x² - x) + 5x³ + (-4x³ + x² - 8)
= (5x³ - 4x³) + (3x² + x²) - x - 8
= x³ + 4x² - x - 8
13. -10(u + v) + 8(u - 1) - 3(u + 6)
= -10u - 10v + 8u - 8 - 3u - 18
= (-10u + 8u - 3u) - 10v + (-8 - 18)
= -5u - 10v - 26
14. 7x - [2(x² - z) + 4x² - 7z] + 6z²
= 7x - (2x² - 2z + 4x² - 7z) + 6z²
= 7x - (6x² - 9z) + 6z²
= 7x - 6x² + 9z + 6z²
= -6x² + 6z² + 7x + 9z