Adding and Subtracting Algebraic Expressions

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

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

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