1. Exercise Make up a fifth-degree monomial with two variables.
Example: 3x 4y

2. Exercise Make up a third-degree trinomial with one variable.
Example: 7x 3 + 5x2 – 4

3. Exercise
Make up a ninth-degree binomial with three different variables.
Example: 4x 5y 3z + 2xy

4. Exercise
Make up a monomial with a degree of zero.
Example: 15

5. Exercise Make up a second-degree binomial with three variables.
Example: 7xy – 2z

6. Like Terms
Like terms are terms that contain an identical variable or variables all raised to the same respective powers.

7. To add polynomials, add like terms using the Commutative, Associative and Distributive Properties.

8. Commutative Property
addition: a + b = b + a
multiplication: ab = ba

9. Associative Property
addition: a + (b + c) = (a + b) + c
multiplication: a(bc) = (ab)c

10. Distributive Property
a(b + c) = ab + ac

11. Example 1 Add (3x + 4) + (2x – 6). (3x + 4) + (2x – 6)

12. Example 2 Add (– 5y + 9z) + (– y – 5z). (– 5y + 9z) + (– y – 5z)
(– 5y – y) + (9z – 5z)
(– 5 – 1)y + (9 – 5)z
– 6y + 4z

13. Example
Add (3x + 4y) + (2x – 2y).
5x + 2y

14. Example
Add (3x + 2) + (4x – 7).
7x – 5

15. Example
Add (4xy + 3x – 1) + (– 3xy + 4y + 2).
xy + 3x + 4y + 1

16. Example 3 Add (3x2 – 10x + 9) + (– 8x2 + 17x – 2).

17. Example 4 Add (3a3 – 8a – 9) + (5a3 + 10a2 + 8).

18. Example
Add (3x2 + 4x – 2) + (– 7x2 + 3x + 1).
– 4x2 + 7x – 1

19. Example
Add (4x2 + 3x – 8) + (11x2 – 5x + 8).
15x2 – 2x

20. Example Add (7x 5 + 3x 4 – 2x2 + 3x + 1) + (4x 4 – 3x 3 + 2x – 5).

21. Example
Add (3x + 7 – x 3) + (2x – 4x).
x3 – x + 8

22. Example
Add (3x 6 + 4x 4 – 2x + 4x2 + x 3 – 1) + (7x 6 + 4x2 – 5 + 7x 3).
10x 6 + 4x 4 + 8x 3 + 8x2 – 2x – 6

23. Example
Add (5x2 – 4x – 3) + (2x2 + 8) + (4x – 7).
7x2 – 2

24. Example 5 Add (2.5x2 + 8.2xy – 4y2) + (3x2 – 0.4xy – 1.5y2).
(2.5x2 + 3x2) + (8.2xy – 0.4xy) + (– 4y2 – 1.5y2)
5.5x xy – 5.5y2

25. Example 6
1 5
3 10
1 10
3 5
Add x x –
1 5
3 10
1 10
3 5
x x –
1 5
1 10
3 10
3 5
x x –

26. Example 6 1 5 3 10 1 10 3 5 Add x + + x – . x + x + – 2 10 1 10 3 10
6 10
3 10
x –
or 0.3x – 0.3

27. Example Add (3.5x2 + 1.27x + 5.3) + (4.9x2 – 3.53x + 1.8).