MAT 105 SPRING 2009 Addition and Subtraction of Algebraic Expressions Section 1.7 Addition and Subtraction of Algebraic Expressions

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”?

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:

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

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

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!

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 ___________.

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

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

Which pairs are like terms?

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.

Perform the indicated operations on the algebraic expressions:

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!

Examples

Examples

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