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Unit 2 - Objective 1 - Addition and Subtraction of Algebraic Expressions


If an algebraic expression consists of parts connected by plus or minus signs, it is called an algebraic sum. Each of the parts of an algebraic sum, together with the sign preceeding it is called an algebraic term. An algebraic term may consist of several factors.  The term 5xy has the individual factors of 5, x, and y.   Other factors are products of two or more of the individual factors.  Terms that involve exactly the same variables to exactly the same power are called like terms.

Each term has two parts. One part is the coefficient and the other part contains the variables.  The coefficient is the product of all of the variables. A variable with no visible coefficient, such as x or y, is understood to have a coefficient of 1.

Examples:

Coefficient of the term 4x2 is 4
Coefficient of the term 18y3z is 18
Coefficient of the term (x2)/3 is 1/3
Coefficient of the term x is 1
Coefficient of the term xy is 1
Coefficient of the term -xy is -1

 

Examples:

7x2y and 4x2y are like terms because they both contain the same variables (x and y). The variable x is raised to the second power and the variable y is raised to the first power.

4xyz3 and 5xyz2 are not like terms because z is raised to the third power in the first term and to the second power in the second term.

In adding and subtracting algebraic expressions, we combine similar (or like) terms into a single term.

Examples:

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