1. To add or subtract polynomials, combine like terms.
Example 1: Adding and Subtracting Monomials
A. 12p3 + 11p2 + 8p Identify like terms.
12p3 + 11p2 + 8p Rearrange terms so that like terms are together.
12p3 + 8p3 + 11p Combine like terms.
20p3 + 11p2
B. 5x2 – 6 – 3x + 8
5x2 – 6 – 3x Identify like terms.
5x2 – 3x + 8 – Rearrange terms so that like terms are together.
5x2 – 3x Combine like terms.
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:
–(2x3 – 3x + 7)= –2x3 + 3x – 7
Example:
(x3 + 4y) – (2x3).
(x3 + 4y) + (–2x3) Rewrite subtraction as addition of the opposite
(x3 + 4y) + (–2x3) Identify like terms.
(x3 – 2x3) + 4y Group like terms together.
–x3 + 4y Combine like terms.

2. 5x2 + 4x + 1 + 2x2 + 5x + 2 7x2 + 9x + 3 5x2 + 4x + 1 + -2x2 - 5x - 2
Polynomials can be added in either vertical or horizontal form.
In vertical form, align the like terms and add or subtract:
(5x2 + 4x + 1) + (2x2 + 5x + 2) (5x2 + 4x + 1) - (2x2 + 5x + 2)
5x2 + 4x + 1
+ 2x2 + 5x + 2
7x2 + 9x + 3
5x2 + 4x + 1
+ -2x2 - 5x - 2
3x2 + 1x - 1
In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms.
(5x2 + 4x + 1) + (2x2 + 5x + 2)
= (5x2 + 2x2 + 1) + (4x + 5x) + (1 + 2)
= 7x2 + 9x + 3