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Simplifying Expressions

The Number Properties - Commutative Property, Associative Property, and Distributive Property - can also be used to simplify algebraic expressions.

Related Topics: More Algebra Lessons



Combining Like Terms

An algebraic expression consisting of two or more like terms can be simplified by combining like terms.

Like terms are terms that have the same variable part i.e. they only differ in their coefficients.

The following diagram shows some examples of like terms. Scroll down the page for more examples and solutions on simplifying expressions by combining like terms.

like terms

Like terms can be added or subtracted from one another.

Example:

Simplify the expressions:

a) 14x + 5x
b) 5y – 13y
c) p – 3p

Solution:

a) 14x + 5x = (14 + 5)x = 19x
b) 5y – 13y = (5 –13)y = –8y
c) p – 3p = (1 – 3)p = – 2p

To simplify an algebraic expression that consists of both like and unlike terms, it might be helpful to first move the like terms together. (When moving the terms, we must remember to move the + or – attached in front of them).

For example,

3x + 2y – 2x + 6
= 3x– 2x + 2y + 6
= (3 – 2)x + 2y + 6
= x + 2y + 6

Example:

Simplify 3x + 2a – 4x

Solution:

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




The following videos show some examples of simplifying expressions by combining like terms. Example:
Simplify
-7ab + 6b - 3ab - 4b - 3ab Example:
Simplify
7xy + 9yz - 3xy - 3yz + 7xy - 2yz Simplify Algebraic Expressions - Combine Like Terms.
Example:
1) 4x3 - 2x2 + 5x3 + 2x - 4x2 - 6x
2) 4y - 2x + 5 - 6y + 7x - 9 Simplify an Algebraic Expression by Combining Like Terms.
This video shows how to simplify a couple of algebraic expressions by combining like terms by adding, subtracting, and using distribution.
Example:
Simplify
a) 4x3 + x2 - 2x3 + 5
b) 10x5 + 3(2x5 - 4b2)

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