Simplifying Expressions
These lessons help students learn how to simplify algebraic expressions. The Number Properties - Commutative Property, Associative Property and Distributive Property - are also used to simplify algebraic expressions.
Related Pages
Solving Linear Equations
Algebraic Expressions
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 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).
Example:
Simplify 3x + 2y – 2x + 6
Solution:
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
Examples:
- 4x3 - 2x2 + 5x3 + 2x - 4x2 - 6x
- 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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