The document describes a lesson on adding and subtracting polynomials. It includes examples of finding the degree of polynomials, adding polynomials by combining like terms, and subtracting polynomials by distributing the negative terms. The examples start simply and increase in complexity, covering the key concepts of adding and subtracting polynomials of various variables and degrees. Student practice problems are provided throughout for students to work through the skills.

1. Adding & Subtracting
Polynomials
Mo du le 9 - To p ic 1

2. What is a Polynomial?
View this Cool Math lesson introducing
Polynomials.
There is only the 1 page of notes.

3. Describe Polynomials
View this Cool Math lesson introducing
terms describing Polynomials.
There are 3 pages of notes.
Be sure to complete the Your Turn problems
in your notebook. Check your answers on
the next slides.

4. Your Turn on Page 3
Find the degree of 3x - x2 .

5. Your Turn on Page 3
Find the degree of 3x - x2 .
The degree is 2.

6. Your Turn on Page 3
Find the degree of 3x - x2 .
The degree is 2.
Find the degree of a 4b - 7a 2b2 .

7. Your Turn on Page 3
Find the degree of 3x - x2 .
The degree is 2.
Find the degree of a 4b - 7a 2b2 .
The degree is 5.

8. Your Turn on Page 3
Find the degree of 3x - x2 .
The degree is 2.
Find the degree of a 4b - 7a 2b2 .
The degree is 5.
Find the degree of 7x - 1.

9. Your Turn on Page 3
Find the degree of 3x - x2 .
The degree is 2.
Find the degree of a 4b - 7a 2b2 .
The degree is 5.
Find the degree of 7x - 1.
The degree is 1.

10. Adding & Subtracting
Polynomials
View this Cool Math lesson to learn how to
add and subtract polynomials.
There are 5 pages of notes.
Be sure to complete the Try It and Your
Turn problems in your notebook. Check
your answers on the next slides.

11. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )

12. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
Remove parenthesis.

13. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
Remove parenthesis.
3x − 4w + z + 6x + 2w + 5z

14. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
Remove parenthesis.
3x − 4w + z + 6x + 2w + 5z
Rearrange so
like terms are
together.

15. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
Remove parenthesis.
3x − 4w + z + 6x + 2w + 5z
Rearrange so
like terms are
together. ( 3x + 6x ) + ( −4w + 2w ) + (1z + 5z )

16. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
Remove parenthesis.
3x − 4w + z + 6x + 2w + 5z
Rearrange so
like terms are
together. ( 3x + 6x ) + ( −4w + 2w ) + (1z + 5z )
Combine like terms.

17. Try It on Page 2
Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
Remove parenthesis.
3x − 4w + z + 6x + 2w + 5z
Rearrange so
like terms are
together. ( 3x + 6x ) + ( −4w + 2w ) + (1z + 5z )
Combine like terms.
9x − 2w + 6z

18. Your Turn on Page 3
Simplify. ( 8x 2
) ( )
− x + 3 + 2x + 6x + 1
2

19. Your Turn on Page 3
Simplify. ( 8x 2
) ( )
− x + 3 + 2x + 6x + 1
2
Remove parenthesis.

20. Your Turn on Page 3
Simplify. ( 8x 2
) ( )
− x + 3 + 2x + 6x + 1
2
Remove parenthesis.
8x − x + 3 + 2x + 6x + 1
2 2

21. Your Turn on Page 3
Simplify. ( 8x 2
) ( )
− x + 3 + 2x + 6x + 1
2
Remove parenthesis.
8x − x + 3 + 2x + 6x + 1
2 2
Rearrange so like
terms are together.

22. Your Turn on Page 3
Simplify. ( 8x 2
) (
− x + 3 + 2x + 6x + 1
2
)
Remove parenthesis.
8x − x + 3 + 2x + 6x + 1
2 2
Rearrange so like
terms are together.
( 8x 2
)
+ 2x + ( −x + 6x ) + ( 3 + 1)
2

23. Your Turn on Page 3
Simplify. ( 8x 2
) (
− x + 3 + 2x + 6x + 1
2
)
Remove parenthesis.
8x − x + 3 + 2x + 6x + 1
2 2
Rearrange so like
terms are together.
( 8x 2
)
+ 2x + ( −x + 6x ) + ( 3 + 1)
2
Combine like terms.

24. Your Turn on Page 3
Simplify. ( 8x 2
) (
− x + 3 + 2x + 6x + 1
2
)
Remove parenthesis.
8x − x + 3 + 2x + 6x + 1
2 2
Rearrange so like
terms are together.
( 8x 2
)
+ 2x + ( −x + 6x ) + ( 3 + 1)
2
Combine like terms.
10x + 5x + 4
2

25. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)

26. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)
Remove parenthesis.

27. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)
Remove parenthesis.
4a b − ab + 3b − 1 + a b + 8ab − 6a + 5
2 2 2 2

28. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)
Remove parenthesis.
4a b − ab + 3b − 1 + a b + 8ab − 6a + 5
2 2 2 2
Rearrange so like terms are together.

29. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)
Remove parenthesis.
4a b − ab + 3b − 1 + a b + 8ab − 6a + 5
2 2 2 2
Rearrange so like terms are together.
( 4a b + a b ) + ( −ab + 8ab ) + 3b
2 2 2
− 6a + ( −1 + 5 )
2

30. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)
Remove parenthesis.
4a b − ab + 3b − 1 + a b + 8ab − 6a + 5
2 2 2 2
Rearrange so like terms are together.
( 4a b + a b ) + ( −ab + 8ab ) + 3b
2 2 2
− 6a + ( −1 + 5 )
2
Combine like terms.

31. Try It on Page 3
Simplify. ( 4a b − ab + 3b
2 2
) (
− 1 + a b + 8ab − 6a + 5
2 2
)
Remove parenthesis.
4a b − ab + 3b − 1 + a b + 8ab − 6a + 5
2 2 2 2
Rearrange so like terms are together.
( 4a b + a b ) + ( −ab + 8ab ) + 3b
2 2 2
− 6a + ( −1 + 5 )
2
Combine like terms.
5a b + 7ab + 3b − 6a + 4
2 2 2

32. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5
2
)

33. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5
2
)
Remove parenthesis but
distribute the negative.

34. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5
2
)
Remove parenthesis but
distribute the negative.
3x − 4x + 8 − x − 7x + 5
2 2

35. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5
2
)
Remove parenthesis but
distribute the negative.
3x − 4x + 8 − x − 7x + 5
2 2
Rearrange so like
terms are together.

36. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5 2
)
Remove parenthesis but
distribute the negative.
3x − 4x + 8 − x − 7x + 5
2 2
Rearrange so like
terms are together.
( 3x 2
−x 2
) + ( −4x − 7x ) + ( 8 + 5 )

37. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5 2
)
Remove parenthesis but
distribute the negative.
3x − 4x + 8 − x − 7x + 5
2 2
Rearrange so like
terms are together.
( 3x 2
−x 2
) + ( −4x − 7x ) + ( 8 + 5 )
Combine like terms.

38. Your Turn on Page 4
Simplify. ( 3x 2
) (
− 4x + 8 − x + 7x − 5 2
)
Remove parenthesis but
distribute the negative.
3x − 4x + 8 − x − 7x + 5
2 2
Rearrange so like
terms are together.
( 3x 2
−x 2
) + ( −4x − 7x ) + ( 8 + 5 )
Combine like terms.
2x − 11x + 13
2

39. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2

40. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.

41. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y
2 2
)

42. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y
2 2
)
Remove parenthesis but
distribute the negative.

43. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y
2 2
)
Remove parenthesis but
distribute the negative.
x − 4xy + 5y − 3x + 6xy − y
2 2 2 2

44. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y
2 2
)
Remove parenthesis but
distribute the negative.
x − 4xy + 5y − 3x + 6xy − y
2 2 2 2
Rearrange so like
terms are together.

45. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y
2 2
)
Remove parenthesis but
distribute the negative.
x − 4xy + 5y − 3x + 6xy − y
2 2 2 2
Rearrange so like
terms are together.
(x 2 2
)
− 3x + ( −4xy + 6xy ) + 5y − y( 2 2
)

46. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y
2 2
)
Remove parenthesis but
distribute the negative.
x − 4xy + 5y − 3x + 6xy − y
2 2 2 2
Rearrange so like
terms are together.
(x 2 2
)
− 3x + ( −4xy + 6xy ) + 5y − y( 2 2
)
Combine like terms.

47. Your Turn on Page 5
Subtract 3x − 6xy + y from x − 4xy + 5y .
2 2 2 2
Write as a subtraction.
(x 2 2
) (
− 4xy + 5y − 3x − 6xy + y 2 2
)
Remove parenthesis but
distribute the negative.
x − 4xy + 5y − 3x + 6xy − y
2 2 2 2
Rearrange so like
terms are together.
(x 2 2
)
− 3x + ( −4xy + 6xy ) + 5y − y ( 2 2
)
Combine like terms.
−2x + 2xy + 4y
2 2

48. Gizmo Practice Activity
Let's practice some more at the Explore Learning
website using the username and password given to
you AND found in the support documents.
Search for the "Addition of Polynomials - Activity
A" Gizmo, launch the Gizmo and try at least 5
problems.
After you have completed at least 5 Gizmo problems,
scroll down to the Assessment Questions and
complete the 4 multiple choice problems.
Pronto or Message me if you have questions.

49. Adding & Subtracting
Polynomials Practice
Practice Adding & Subtracting Polynomials at this Cool
Math website.
Select the “Give me a Problem” button to keep trying
problems.
Do your work in a notebook.
When you select “What’s the Answer?” your answer is
erased and correct answer is displayed. Having your
work in a notebook will allow you to compare your
answer to the correct answer.
Keep working problems until you get 4 out of 5 correct.

50. Way to Go!
You’ve finished reviewing
the notes for Adding and
Subtracting Polynomials.
Proceed to Module 9 Topic 1 Mastery
Assignment.