36 Chapter 1 Real Numbers and Algebraic Expressions So, 4x + 2x = (4 + 2)x = 6x Note that combining like terms is based on the distributive property since ab + ac = a(b + c) or (b + c)a. Procedure: Simplifying Algebraic Expressions Step 1: Remove any parentheses by applying the distributive property. Step 2: Apply the commutative property to group like terms together. Step 3: Combine any like terms. Objective 3 Examples Simplify each expression. 3a. 4y - 9 + 2y 3b. x2 - x - x + 1 3c. a3 + 2a2 + 4a - 2a2 - 4a - 8 3d. 0.05x + 0.03(10,000 - x) 3e. 3 - 5( y - 2) 3f. 12a2b - 7 6 b - 12ab - 5 4 b Solutions 3a. 4y - 9 + 2y = 4y + 2y - 9 Apply the commutative property of addition. = (4 + 2)y - 9 Apply the distributive property to add like terms. = 6y - 9 Simplify. 3b. x2 - x - x + 1 = x2 + -1x - 1x + 1 Recall -x = -1x. = x2 + (-1 - 1) x + 1 Apply the distributive property to add like terms. = x2 - 2x + 1 Simplify. 3c. a3 + 2a2 + 4a - 2a2 - 4a - 8 = a3 + 2a2 - 2a2 + 4a - 4a - 8 Apply the commutative property of addition. = a3 + (2 - 2)a2 + (4 - 4)a - 8 Apply the distributive property to add like terms. = a3 + 0a2 + 0a - 8 Simplify. = a3 - 8 Simplify. 3d. 0.05x + 0.03(10,000 - x) Apply the distributive property. = 0.05x + 300 - 0.03x Apply the commutative property of addition. = (0.05 - 0.03) x + 300 Apply the distributive property to add like terms. = 0.02 x + 300 Simplify. 3e. 3 - 5(y - 2) = 3 - 5y + 10 Apply the distributive property. = -5y + 3 + 10 Apply the commutative property of addition. =-5y + 13 Simplify.
hendricks_intermediate_algebra_1e_ch1_3
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