Pre-Algebra Demystified

Monomials: 3x^2 
5y 2x^3 y^2

Binomials: xþ2y 3x^2 þx 
2yþz

Trinomials 3x^2 þ4x
12x
3yþ 5

Addition of Polynomials

Recall in Chapter 7 that only like terms can be added or subtracted. For

example, 5xþ6x¼11x. Unlike terms cannot be added or subtracted.

To add two or more polynomials, add like terms.

EXAMPLE

Add (3x^2 þ2x
5)þ(5x^2 
7xþ3).

SOLUTION

ð3x^2 þ2x
 5 Þþð5x^2 
7xþ 3 Þ¼3x^2 þ2x
 5 þ5x^2 
7xþ 3

¼ð3x^2 þ5x^2 Þþð2x
7xÞþð
 5 þ 3 Þ

¼8x^2 
5x
 2

Math Note: Recall that when the numerical coefficient is one, it is

not written: i.e., xy¼1xy. Likewise
xy¼
1xy.

EXAMPLE

Add (2xþy)þ(2x
5)þ(3y
7).

SOLUTION

ð2xþyÞþð2x
 5 Þþð3y
 7 Þ¼2xþyþ2x
 5 þ3y
 7

¼ð2xþ2xÞþðyþ3yÞþð
 5 
 7 Þ

¼4xþ4y
 12

Math Note: If the sum of two like terms is 0, do not write the term

in the sum.

234 CHAPTER 12 Monomials and Polynomials