1. The document discusses polynomials, including adding and subtracting polynomials. It defines important terms used in working with polynomials like monomial, binomial, trinomial, coefficient, constant, and like terms. 2. Examples are provided for writing polynomials in standard form, adding polynomials, subtracting polynomials, and simplifying polynomials. 3. Homework assigned is problems 1-39 odd on page 378.

1. Chapter 9
Polynomials

2. Section 9-1
Add and Subtract Polynomials

3. Essential Questions
How do you write polynomials in standard form?
How do you add and subtract polynomials?
Where you’ll see this:
Part-time jobs, travel, geography, modeling

4. Vocabulary
1. Monomial:
2. Coefficient:
3. Constant:
4. Polynomial:
5. Term:

5. Vocabulary
1. Monomial: An expression that has one term (a
number, variable, or a combination of both a
number and variables without any addition or
subtraction)
2. Coefficient:
3. Constant:
4. Polynomial:
5. Term:

6. Vocabulary
1. Monomial: An expression that has one term (a
number, variable, or a combination of both a
number and variables without any addition or
subtraction)
2. Coefficient: The number that is with the variable
3. Constant:
4. Polynomial:
5. Term:

7. Vocabulary
1. Monomial: An expression that has one term (a
number, variable, or a combination of both a
number and variables without any addition or
subtraction)
2. Coefficient: The number that is with the variable
3. Constant: A number without a variable
4. Polynomial:
5. Term:

8. Vocabulary
1. Monomial: An expression that has one term (a
number, variable, or a combination of both a
number and variables without any addition or
subtraction)
2. Coefficient: The number that is with the variable
3. Constant: A number without a variable
4. Polynomial: A collection of terms that are
combined by addition or subtraction
5. Term:

9. Vocabulary
1. Monomial: An expression that has one term (a
number, variable, or a combination of both a
number and variables without any addition or
subtraction)
2. Coefficient: The number that is with the variable
3. Constant: A number without a variable
4. Polynomial: A collection of terms that are
combined by addition or subtraction
5. Term: Each monomial within a polynomial

10. Vocabulary
6. Binomial:
7. Trinomial:
8. Standard Form:
9. Like Terms:

11. Vocabulary
6. Binomial: A polynomial with two terms
7. Trinomial:
8. Standard Form:
9. Like Terms:

12. Vocabulary
6. Binomial: A polynomial with two terms
7. Trinomial: A polynomial with three terms
8. Standard Form:
9. Like Terms:

13. Vocabulary
6. Binomial: A polynomial with two terms
7. Trinomial: A polynomial with three terms
8. Standard Form: When a polynomial is written from
highest to lowest degree (highest to lowest
exponent)
9. Like Terms:

14. Vocabulary
6. Binomial: A polynomial with two terms
7. Trinomial: A polynomial with three terms
8. Standard Form: When a polynomial is written from
highest to lowest degree (highest to lowest
exponent)
9. Like Terms: Terms that have the same variable
parts (variables and exponents)

15. Example 1
Tell the variable for which the polynomial is
arranged in standard form.
3 2
a. 2a + 3ab − 4b
3 2
b. 2(a + b) + 3(a + b) − 4(a + b) + 7

16. Example 1
Tell the variable for which the polynomial is
arranged in standard form.
3 2
a. 2a + 3ab − 4b
a
3 2
b. 2(a + b) + 3(a + b) − 4(a + b) + 7

17. Example 1
Tell the variable for which the polynomial is
arranged in standard form.
3 2
a. 2a + 3ab − 4b
a
3 2
b. 2(a + b) + 3(a + b) − 4(a + b) + 7
(a + b)

18. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )

19. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2
2x − 3x + 7 − 2x − 8 + x − 7x
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )

20. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2
2x − 3x + 7 − 2x − 8 + x − 7x
2
3x
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )

21. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2
2x − 3x + 7 − 2x − 8 + x − 7x
2
3x −12x
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )

22. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2
2x − 3x + 7 − 2x − 8 + x − 7x
2
3x −12x −1
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )

23. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2
2x − 3x + 7 − 2x − 8 + x − 7x
2
3x −12x −1
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
2 2 2 2
3x − 4 xy − x + 4 y + 2xy − y

24. Example 2
Add the polynomials.
2 2
a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x)
2 2
2x − 3x + 7 − 2x − 8 + x − 7x
2
3x −12x −1
2 2 2 2
b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
2 2 2 2
3x − 4 xy − x + 4 y + 2xy − y
2 2
2x − 2xy + 3y

25. Example 3
Subtract 4x + y from the sum of x + 3y and 8x - 2y.

26. Example 3
Subtract 4x + y from the sum of x + 3y and 8x - 2y.
( x + 3y ) + (8 x − 2y ) − (4 x + y )

27. Example 3
Subtract 4x + y from the sum of x + 3y and 8x - 2y.
( x + 3y ) + (8 x − 2y ) − (4 x + y )
x + 3y + 8 x − 2y − 4 x − y

28. Example 3
Subtract 4x + y from the sum of x + 3y and 8x - 2y.
( x + 3y ) + (8 x − 2y ) − (4 x + y )
x + 3y + 8 x − 2y − 4 x − y
5x

29. Example 4
Simplify.
3 2 3 2
a. (6 x + 3x − 11x) + (2x − 9 x − 5 x)
2 2 2 2
b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)

30. Example 4
Simplify.
3 2 3 2
a. (6 x + 3x − 11x) + (2x − 9 x − 5 x)
3 2 3 2
6 x + 3x − 11x + 2x − 9 x − 5 x
2 2 2 2
b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)

31. Example 4
Simplify.
3 2 3 2
a. (6 x + 3x − 11x) + (2x − 9 x − 5 x)
3 2 3 2
6 x + 3x − 11x + 2x − 9 x − 5 x
3 2
8 x − 6 x − 16 x
2 2 2 2
b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)

32. Example 4
Simplify.
3 2 3 2
a. (6 x + 3x − 11x) + (2x − 9 x − 5 x)
3 2 3 2
6 x + 3x − 11x + 2x − 9 x − 5 x
3 2
8 x − 6 x − 16 x
2 2 2 2
b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
2 2 2 2
x y − 2xy + 8 + 7x y − 2xy + 4

33. Example 4
Simplify.
3 2 3 2
a. (6 x + 3x − 11x) + (2x − 9 x − 5 x)
3 2 3 2
6 x + 3x − 11x + 2x − 9 x − 5 x
3 2
8 x − 6 x − 16 x
2 2 2 2
b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
2 2 2 2
x y − 2xy + 8 + 7x y − 2xy + 4
2 2
8 x y − 4 xy + 12

34. Example 4
Simplify.
2 2 2 2 2
c. ( x y + x − xy ) − (− y + y + xy + 4 x y )

35. Example 4
Simplify.
2 2 2 2 2
c. ( x y + x − xy ) − (− y + y + xy + 4 x y )
2 2 2 2 2
x y + x − xy + y − y − xy − 4 x y

36. Example 4
Simplify.
2 2 2 2 2
c. ( x y + x − xy ) − (− y + y + xy + 4 x y )
2 2 2 2 2
x y + x − xy + y − y − xy − 4 x y
2 2 2
−3x y + x − 2xy + y − y

37. Homework

38. Homework
p. 378 #1-39 odd
“Deeds, not stones, are the true monuments of the
great.” - John L. Motley