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Adding and Subtracting Algebraic Expressions




In these lessons, we will learn how to simplify expressions by adding or subtracting like terms (combining like terms).

Related Topics: More Algebra Lessons

Simplifying Expressions Of Like Terms

An algebraic expression consisting of like terms can be simplified by adding or subtracting the coefficients of the like terms.

Example:

Simplifying the expressions:

a) 14x + 5x

b) 5y – 13y

c) p – 3p

d)

Solution:

a) 14x + 5x = (14 + 5)x = 19x

b) 5y – 13y = (5 –13)y = –8y

c) p – 3p = (1 – 3)p = – 2p

d)



 

Simplifying Expressions Of Like and Unlike Terms

To simplify an algebraic expression that consists of both like and unlike terms, we need to

Step 1: move the like terms together
Step 2: add or subtract their coefficients.

When moving the terms, we must remember to move the + or – attached in front of them. For example,





 

Example:

Simplify 3x + 2a – 4x

Solution:

3x + 2a – 4x
= 3x + 2a –4x
= 3x – 4x + 2a
= –x + 2a

Example:

Simplify b + 1.4c - 0.6b + 2

Solution:

b + 1.4c - 0.6b + 2
= b + 1.4c - 0.6b + 2
= b – 0.6b + 1.4c + 2
= 0.4 b + 1.4 c + 2




 

This video explains how to add, subtract, combine like terms in algebraic expressions.


The following video shows how to add and subtract algebraic terms or variables.




This video gives more examples of combining like terms.


Simplify an Algebraic Expression by Combining Like Terms.
This video shows how to simplify algebraic expressions by combining like terms by adding, subtracting, and using distribution.



 


You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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