Section 1.8 Algebraic Expressions 77 �� ���������������� �������� Algebraic Expressions In the previous sections, we have evaluated algebraic expressions and also expressed relationships mathematically as algebraic expressions. We will now discuss these types of expressions in more detail and learn some terminology that we use to describe them. Terminology Dealing with Algebraic Expressions A term is a number or a product of a number and variables raised to exponents. Terms are separated by addition or subtraction signs. Algebraic expressions consist of variable terms and constant terms. Variable terms are terms that contain a variable. Constant terms do not contain variables. Each variable term has a numerical coefficient. The coefficient is the number that is multiplied by the variable. 3x2 -5x + 7 { { { Variable term Constant term ���������������������� Identifying Terms and Coefficients of an Algebraic Expression Step 1: Determine how many expressions are connected by an addition or subtraction sign. This gives us how many terms the expression contains. a. The terms with variables are the variable terms. b. The terms with numbers only are the constant terms. Step 2: The coefficients of the variable terms are the numbers multiplied by the variable. Be careful to identify the sign of the coefficient. If the variable term is connected by a subtraction sign, then the coefficient of that term is a negative value. Remember that subtraction is adding the opposite. Also, remember the Identity Property of Multiplication: x = 1 · x. �� ������������������������ ������������������ Complete the table to identify the number of terms, the variable terms, the constant terms, and the coefficients of the variable terms of each expression. Expression Total Number of Terms Variable Term(s) Constant Term(s) Coefficients of Each Variable Term 1a. 2x 1 2x None 2 1b. -x 1 -x = -1x None -1 1c. x + 2 2 x = 1x 2 1 1d. y 2 - 5 2 y 2 = 1y 2 = 1 2 y -5 1 2 1e. 3x2 - 5x + 7 3 3x2, -5x 7 3, -5 1f. -2y3 + 3y2 - y - 6 4 -2y3, 3y2, -y -6 -2, 3, -1 Student Check 1 Complete the table to identify the number of terms, the variable terms, the constant terms, and the coefficients of the variable terms of each expression. Expression Total Number of Terms Variable Term(s) Constant Term(s) Coefficients of Each Variable Term a. 7a b. -y c. x - 7 d. x 3 - 4 e. 6y2 - y + 3 f. 4y3 - y2 + 2y - 1 Objective 1�� ▶ Identify terms and coefficients of algebraic expressions. Coefficients Variable term ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Identify terms and coefficients of algebraic expressions. 2. Identify like terms. 3. Combine like terms. 4. Simplify algebraic expressions. 5. Troubleshoot common errors.
hendricks_beginning_algebra_1e_ch1_3
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