1. Adding and Subtracting, Polynomials
August 10, 2016

2. Essential question
How do I add or subtract polynomials?

3. Outline Vocabulary Review Like Terms Adding Polynomials
Subtracting Polynomials

4. Vocabulary review Monomial expression Binomial expression
Expression with one term 5x
7y2
Binomial expression
Expression with 2 terms
4xy + 9z
12ab + 14cd
Polynomial expression
Expression with more than 2 terms
8x3 + 12x2 – 4x + 6
12x2 + 14x -16

5. Like Terms
Like Terms
Unlike Terms
2x, 45x, x, -26x, -x
17x, 17z
15, -2, 27, 9043, 0.6
15y, 19y2, 31y5
3y2, y2, -y2, 26y2
19x, 14xy

6. Adding Polynomials
Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a)
Step 1: Group all like terms together
(9y-3y) +(-7x+8x) +(15a-8a)
6y + x +7a
Step 2: Make sure the expression is standard form (i.e. decreasing degree order if the same variable is used)
Doesn’t apply in above example

7. Adding Polynomials
Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)
Step 1: Group all like terms together
3a2 + (3ab + 4ab) + (- b2 + 6b2)
3a2 + 7ab + 5b2
Step 2: Make sure the expression is standard form (i.e. decreasing degree order if the same variable is used)
Doesn’t apply in above example

8. Adding Polynomials x2 + 3x + 7y + xy + 8 x2 + 4y + 2x + 3 3x + 7y + 81 1 Y 1 1 1 Y 1 1 1 Y
x2 + 3x + 7y + xy + 8
x2 + 4y + 2x + 3
3x + 7y + 8
x2 + 11xy + 8

9. Adding Polynomials (Alternate Method)
Add the following polynomials using column form: (4x2 – 2xy + 3y2) + (-3x2 –xy + 2y2)
(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
Line up your like terms
4x2 - 2xy + 3y2
+ -3x2 - xy + 2y2
X2 -3xy + 5y2

10. Subtracting Polynomials
Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)
Step 1: Rewrite subtraction as adding the opposite.
(9y - 7x + 15a) + (+ 3y - 8x + 8a)
Step 2: Group the like terms.
(9y + 3y)+ (- 7x - 8x) + (15a + 8a)
12y-15x+23a

11. Subtracting Polynomials
Subtract the following polynomials: (7a - 10b) - (3a + 4b)
Step 1: Rewrite subtraction as adding the opposite.
(7a – 10b) + (- 3a – 4b)
Step 2: Group the like terms.
(7a - 3a)+ (- 10b – 4b)
4a -14b

12. subtracting Polynomials (Alternate Method)
Add the following polynomials using column form: (4x2 – 2xy + 3y2) - (-6x2 +5xy - 7y2)
(4x2 - 2xy + 3y2) + (6x2 - 5xy + 7y2)
Line up your like terms
4x2 - 2xy + 3y2
+ 6x2 - 5xy + 7y2
10X2 -7xy + 10y2

13. Examples Find the sum or difference. (5a – 3b) + (2a + 6b) 3a – 9b

14. Examples Find the sum or difference. (5a – 3b) – (2a + 6b) 3a – 9b