Simplifying Expressions

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

Combining Like Terms

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

For example:

2x and –5x are like terms

a and are like terms

6x and 5y are unlike 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

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