Easy Algebra Step-by-Step

88 Easy Algebra Step-by-Step

Addition and Subtraction of Monomials

Because variables are standing in for real numbers, you can use the proper-

ties of real numbers to perform operations with polynomials.

Addition and Subtraction of Monomials

1. To add monomials that are like terms, add their numerical coeffi -
   cients and use the sum as the coeffi cient of their common variable
   component.


2. To subtract monomials that are like terms, subtract their numerical
   coeffi cients and use the difference as the coeffi cient of their common
   variable component.


3. To add or subtract unlike terms, indicate the addition or subtraction.

Problem Simplify.

a. −+ 10 xx+ 2525

b. 47 xy^23 xy^323

c. 9 xx^2233333 x^2 − 7 x^2

d. 25 + 25 x

e. 5 xx^22777

Solution

a. −+ 10 xx+ 2525

Step 1. Check for like terms.

−+ 10 xx+ 2525

− 10 x and 25 x are like terms.

Step 2. Add the numerical coeffi cients.

−+ 10 25 = 15

Step 3. Use the sum as the coeffi cient of x.

−+ 10 xx+ 2525 = 15 x

b. 47 xy^23 xy^323

Step 1. Check for like terms.

47 xy^23 xy^32

P

−+ 10 xx+ 2525 ≠ 15 x^2. In addition

and subtraction, the exponents

on the variables do not change.