This document defines polynomials and their terms. It discusses adding and subtracting polynomials by combining like terms. To add polynomials, the coefficients of like terms are added while the variables stay the same. There are two methods for adding polynomials - vertical alignment of like terms or regrouping terms using properties. Subtraction of polynomials is performed by changing the operation to addition of the opposite polynomial. Examples demonstrate adding and subtracting polynomials step-by-step.

1. ADDING AND SUBTRACTING
POLYNOMIALS

2. Definition of Terms
POLYNOMIAL
• Is an algebraic expression that represent a sum of one or more terms
containing whole number and exponents on the variables.
MONOMIAL
• It is a polynomial with only one term. E.g., 2x, 3𝑥2
, 2, ab, 42xyz
BINOMIAL
• It is a polynomial with two terms. E.g., 2x + 7, 3𝑐2+ a, 4xz + 2yd
TRINOMIAL
• It is a polynomial with three terms. E.g., a + b + c, 2𝑥2
+ 3y + 6, 2x + 2xy +
4y

3. We group as one!

4. We group as one!

5. •You can only combine terms together if they
are LIKE TERMS.
•If they are not like terms, you must keep
them separate.

6. 2x + 3y + 4x
Let x be a circle, and y be a triangle.
2x + 3y + 4x
= 6x + 3y

7. ADDITION OF POLYNOMIALS
To add like terms together, you add the coefficients and
keep the variable part the same.
4x + 3x = 7x
Add the
coefficients.
The variable part
stays the same.

8. ADDITION OF POLYNOMIALS
There are two (2) common methods by which we add
algebraic expressions.
For example:
(7xy + 5yz – 3xz) + (4yz + 9xz – 4y) + (-2xy – 3xz + 5x)

9. METHOD 1
In Vertical form, align the like terms and add.
(7xy + 5yz – 3xz) + (4yz + 9xz – 4y) + (-2xy – 3xz + 5x)
7xy + 5yz – 3xz
+ 4yz + 9xz - 4y
+ -2xy - 3xz + 5x
5xy + 9yz + 3xz + 5x – 4y

10. METHOD 2
In horizontal form, use the Associative and Commutative
Properties to regroup and combine like terms.
(7xy + 5yz – 3xz) + (4yz + 9xz – 4y) + (-2xy – 3xz + 5x)
= (7xy – 2xy) + (5yz + 4yz) + (-3xz + 9xz – 3xz) + 5x – 4y
= 5xy + 9yz + 3xz + 5x – 4y

11. Example 1: Adding Polynomials
A. (4𝑚2+ 5) + (𝑚2 - m + 6)
= (4𝑚2+ 5) + (𝑚2 - m + 6) Identify like terms
= (4𝑚2+ 𝑚2) + (-m) + (5 + 6) Group like terms together
= 5𝒎𝟐 - m + 11 Combine like terms
B. (10xy + x) + (-3xy + y)
= (10xy + x) + (-3xy + y) Identify like terms
= (10xy – 3xy) + x + y Group like terms together
= 7xy + x + y Combine like terms

12. Example 2: Adding Polynomials
(6 𝑥2 - 4y) + (3 𝑥2 + 3y - 8 𝑥2 - 2y)
=(6 𝑥2 - 4y) + (3 𝑥2 + 3y - 8 𝑥2 - 2y) Identify like terms.
=(6 𝑥2
- 4y) + (-5 𝑥2
+ y) Combine like terms in the second
polynomials
=(6 𝑥2 - 5 𝑥2) + (-4y + y) Combine like terms
= 𝑥2 - 3y + 8 𝑥2 - 2y Simplify.
= (𝑥2 + 8 𝑥2 ) + (-3y -2y)
=9 𝑥2 - 5y

13. You try!
1. (3 𝑥2
+ 5 – 2x) + (5x + 4 𝑥2
- 2) =
2. (-8x + 𝑥2 + 4) + (-3 𝑥2 + 5x – 6) =

14. SUBTRACTION OF POLYNOMIALS
To subtract polynomials, remember that subtracting is the same as
adding the opposite. To find the opposite of a polynomial, you
must write the opposite of each term in the polynomial:
For example:
- (2 𝑥3
- 3x + 7) = -2 𝑥3
+ 3x - 7

15. Example 1: Subtracting Polynomials
Subtract.
= (𝑥3
+ 4y) – (2 𝑥3
)
= (𝑥3 + 4y) + (-2 𝑥3) Rewrite the subtraction as
addition of the opposite
= (𝑥3 + 4y) + (-2 𝑥3) Identify like terms
= (𝑥3 - 2 𝑥3) + 4y Group like terms together
= - 𝒙𝟑
+ 4y Combine like terms

16. Example 2: Subtracting Polynomials
Subtract.
= (7𝑚4
- 2𝑚2
) – (5𝑚4
- 5𝑚2
+ 8)
= (7𝑚4 - 2𝑚2) + (-5𝑚4 + 5𝑚2 - 8) Rewrite the subtraction as
addition of the opposite
= (7𝑚4 - 2𝑚2) + (-5𝑚4 + 5𝑚2 - 8) Identify like terms
= (7𝑚4 - 5𝑚4) + (-2𝑚2 + 5𝑚2) - 8 Group like terms together
= 2𝒎𝟒
+ 3 𝒎𝟐
- 8 Combine like terms

17. Example 3: Subtracting Polynomials
Subtract.
= (-10𝑥2
- 3x + 7) – (𝑥2
- 9)
= (-10𝑥2 - 3x + 7) + (-𝑥2 + 9) Rewrite the subtraction as
addition of the opposite
= (-10𝑥2 - 3x + 7) + (-𝑥2 + 9) Identify like terms
-10𝑥2 - 3x + 7 Use the vertical method.
-𝑥2 + 0x + 9 Write 0x as a placeholder.
-11𝒙𝟐 - 3x + 16 Combine like terms

18. You try!
1. (6 𝒙𝟐 + 11x – 3) – (3 𝒙𝟐 - 5x + 9) =
2. (𝒙𝟐 + 7x – 7) – (3 𝒙𝟐 + 5x – 3) =