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**MAT 105 SPRING 2009 Addition and Subtraction of Algebraic Expressions**

Section 1.7 Addition and Subtraction of Algebraic Expressions

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**Algebraic Expression:**

Any combination of numbers and literal symbols (variables) involving one or more algebraic operations What is the difference between an algebraic expression and an equation? For example: What is the difference between the terms “simplify” and “solve”?

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**Term: A term is one part of an algebraic expression.**

It can contain a number and one or more variables and may involve multiplication, division, radicals, and exponents. Terms are separated from one another in an expression by an addition or subtraction symbol. Example:

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**Factors: Multinomial:**

The quantities (numbers or literal symbols) that are being multiplied together. Multinomial: Any algebraic expression containing two or more terms.

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Polynomial: A term or a finite sum of terms, with only whole number exponents on the variables. For example:

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**These are NOT polynomials!**

The terms of a polynomial cannot have a variable under a radical or a variable in the denominator. These are NOT polynomials!

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**Classifying polynomials**

A polynomial (or multinomial) containing three terms is a ________________. A polynomial (or multinomial) containing two terms is a ________________. A single-term polynomial is called a ___________.

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**Numerical Coefficient**

of a term is the number (or product of numbers) that is being multiplied by the variable.

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Like Terms: Terms that differ at most in their numerical coefficients are called like terms. Like terms have the same ______________ raised to the same ______________.

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**Which pairs are like terms?**

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**To add or subtract algebraic expressions:**

Combine like terms into a single term by adding or subtracting the numerical coefficients of the like terms. An algebraic expression in simplest form will contain only terms that are unlike.

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**Perform the indicated operations on the algebraic expressions:**

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**Grouping Symbols, revisited**

( ) [ ] { } If grouping symbols are nested, work from the inside outward. And remember, if you have a grouping symbol preceded by a subtraction sign, you must change the sign of every term within the grouping symbol!

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Examples

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Examples

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More Practice Text p 29 # 26, 32, 38, 46

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