1. (Combining Like Terms)
Lesson 9-1
Adding and Subtracting Polynomials.
(Combining Like Terms)
Designed by Skip Tyler, Varina High School

2. Definitions you’ll need:
nomial – term
mono – bi – tri – 3
degree – highest exponent you have
1 – linear – quadratic 3 – cubic

3. Applying the Definitions:
Examples of:
monomials
binomials
trinomials
2x or 4y or 6
(just one term)
2x + 4 or y – 8
(two terms)
3x2 + 2x – 4 or 2x + y – 4
(three terms)

4. Applying the Definitions:
Examples of:
linear
quadratic
cubic
2x or 4y + 2
(highest power is 1)
3x2 + 2x – 4
(highest power is 2)
2g3 + 3g2 + 2g – 4
(highest power is 3)

5. Look at the table on pg. 457 in your book!

6. Another way to look at naming… (Pick one from each column)
First Name by Exponent
Middle Name by Terms
Last Name
Linear (1st degree)
Mono (1)
NOMIAL
*They all have the same last name.
Quadratic (2nd degree)
Bi (2)
Cubic (3rd degree)
Tri (3)
______ degree
(4 and up)
Poly (4 and up)

7. Classified by number of terms
More Examples…
Classified by number of terms
Classified by degree
Polynomial
Degree 6
constant
monomial
–2 x 1
linear
monomial
3x + 1 1
linear
binomial
–x x – 5 2
quadratic
trinomial
4x 3 – 8x 3
cubic
binomial
2 x 4 – 7x 3 – 5x + 1 4
fourth degree
polynomial

8. Let’s look at how to… Add and Subtract Polynomials
Remember to combine like terms!!!

9. 1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a)
Group your like terms.
9y - 3y - 7x + 8x + 15a - 8a
6y + x + 7a

10. 2. Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)
Combine your like terms.
3a2 + 3ab + 4ab - b2 + 6b2
3a2 + 7ab + 5b2

11. 3. Add the following polynomials using column form: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
Line up your like terms.
4x2 - 2xy + 3y2
+ -3x2 - xy + 2y2
_________________________
x2 - 3xy + 5y2

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

13. 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b)
Rewrite subtraction as adding the opposite.
(7a - 10b) + (- 3a - 4b)
Group the like terms.
7a - 3a - 10b - 4b
4a - 14b

14. Line up your like terms and add the opposite.
6. Subtract the following polynomials using column form: (4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)
Line up your like terms and add the opposite.
4x2 - 2xy + 3y2
+ (+ 3x2 + xy - 2y2)
7x2 - xy + y2

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

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