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hendricks_beginning_algebra_1e_ch1_3

Section 1.8 Algebraic Expressions 81 5c. Simplify 4 - 3(x - 2). �������������������������������������� ���������������������������������������������������������������� 4 - 3( x - 2) 1(x 2) x - The distributive property must be applied first because, according to the order of operations, multiplication comes before addition or subtraction. After distributing, we can combine like terms. 4 - 3(x - 2) 4 - 3x + 6 -3x + 4 + 6 -3x + 10 - 2 Student Check 2 a. unlike b. like c. like d. unlike Student Check 3 a. 12y b. 9b c. 11a2 d. can’t be combined e. 13 3 a f. -7x2 + x Student Check 4 a. 2y - 8 b. 30x + 11 c. 38x - 6 d. -6x - 7 1. A term is a number or a product of a number and a variable raised to exponents. The terms in an algebraic expression are separated by addition or subtraction. The coefficient of a variable term is the number multiplied by the variable. Remember that a variable by itself is understood to have a coefficient of 1 since 1 · x = x. 2. Like terms are terms with the same variables and same exponents. 3. To combine like terms, combine the coefficients of the like terms and keep the variable the same. 4. To simplify an algebraic expression, clear any parentheses by applying the distributive property and then combine like terms. ANSWERS TO STUDENT CHECKS Expression Total Number of Terms Variable Term(s) Constant Term(s) Coeffi cients of Each Variable Term Student Check 1 a. 7a 1 7a None 7 b. -y 1 -y None -1 c. x - 7 2 x -7 1 d. x 3 - 4 2 1 3 x -4 1 3 e. 6y2 - y + 3 3 6y2, -y 3 6, -1 f. 4y3 - y2 + 2y - 1 4 4y3, -y2, 2y -1 4, -1, 2 SUMMARY OF KEY CONCEPTS �� ���������������� �������� EXERCISE SET Write About It! Use complete sentences to explain each term or process. 1. Difference of a variable term and a constant term 2. Numerical coefficient 3. Terms and coefficients of an algebraic expression 4. Like terms 5. How to apply the distributive property to combine like terms 6. How to simplify an algebraic expression 7. Determine if the following statement is true or false: An algebraic expression must have a variable term. 8. Determine if the following statement is true or false; if false, explain the error: -2(3x - 4) = -6x - 8


hendricks_beginning_algebra_1e_ch1_3
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