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.
An algebraic expression consisting of two or more like terms can be simplified by combining like terms.
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.
Simplify the expressions:
a) 14x + 5x
b) 5y – 13y
c) p – 3p
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).
Simplify 3x + 2y – 2x + 6
3x + 2y – 2x + 6
= 3x– 2x + 2y + 6
= (3 – 2)x + 2y + 6
= x + 2y + 6
Simplify 3x + 2a – 4x
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.
Simplify -7ab + 6b - 3ab - 4b - 3ab
Simplify 7xy + 9yz - 3xy - 3yz + 7xy - 2yz
Simplify Algebraic Expressions - Combine Like Terms
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.
a) 4x3 + x2 - 2x3 + 5
b) 10x5 + 3(2x5 - 4b2)
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