Add and Subtract Polynomials

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