1. Exercise
Find the opposite (additive inverse) of 4.3.
– 4.3

2. Exercise
Find the opposite (additive inverse) of – 27. 27

3. Exercise
Find the opposite (additive inverse) of x.
– x

4. Exercise
Find the opposite (additive inverse) of 3y.
– 3y

5. Exercise
Find the opposite (additive inverse) of 7z – 16.
– 7z + 16

6. Additive Inverse
Polynomial
3x + 4
– 3x – 4
2y – 6
– 2y + 6
– x2 + 2x – 5
x2 – 2x + 5

7. Example 1 Find the opposite of x2 – 3x + 4. – (x2 – 3x + 4)

8. Example
Find the opposite of 3x – 2.
– 3x + 2

9. Example
Find the additive inverse of x3 – 4x + 3.
– x3 + 4x – 3

10. Example
Find the additive inverse of 4xy – 3z2.
– 4xy + 3z2

11. Example 2 Subtract 15x – (– 2x – 8y). 15x – (– 2x – 8y)

12. Example 3 Subtract (5x – 2y) – (3x + 4y). (5x – 2y) – (3x + 4y)
= (5x – 3x) + (– 2y – 4y)
= 2x + (– 6y)
= 2x – 6y

13. Example
Subtract 9x – (2x + 3).
7x – 3

14. Example
Subtract (12x + 5) – (8x + 3).
4x + 2

15. Example 4 Subtract (8x2 – 9x – 3) – (2x2 + 6x – 4).

16. Example 5 Subtract (x3 + 2x2 – 9x + 14) – (7x2 – 6x – 4).

17. Example 6 Subtract (2x3 – 1) – (6x2 + 8x). (2x3 – 1) – (6x2 + 8x)

18. Example
Subtract (3a + 2b – 5) – (2a – 2b + 5).
a + 4b – 10

19. Example Subtract (x3 + 6x2 – 7x + 4) – (2x3 + x2 + 3x – 8).

20. Example Subtract (8x3 + 5x – 7) – (x4 + 3x3 – x2 + 1).

21. Example
Arrange the polynomials in descending powers of the variable, and then subtract: (3x – 4x2 + 2) – (2x + 5x2 + 3).
– 9x2 + x – 1

22. Example Subtract: (x5 – 3x2 + 1 + 4x3) – (x4 – 5x + x2 – 2x3).

23. Exercise Subtract: (2x – 8x4 + 7x2 – 9x3) – (8x2 – 4x3 – 3x + x4).

24. Exercise Subtract: (5 – x3 + 8x – 2x2) – (4x2 – 7 + 9x – 5x3).

25. Exercise
Set up the problem vertically and subtract by using the definition of subtraction: (4a + 2b – 7c) – (– 6a + 3b + 9c).
10a – b – 16c

26. Exercise
Set up the problem vertically and subtract by using the definition of subtraction: (6x2 – 9x + 4) – (– 3x2 – 12x – 5).
9x2 + 3x + 9