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12 algebraic expressions Objectives: Title: Jun 256:00 PM (1 of 8) To evaluate algebraic expressions To simplify algebraic expressions ��������������������������� Use the order of operations to simplify each expression. . . 1. 8 3 2 4 .. _ 2. 8 4 + 6 3 .. . .. _ _ 3. 24 12 4 3 * for help turn to page 873 Title: Jun 256:03 PM (2 of 8) _. . . 4. 3 8 + 12 4 2 .. _ 2 5. 27 + 18 9 3 + 1 . _ . 6. (40 + 24) 8 (2 + 1 ) 3 Vocabulary variable algebraic expression (variable expression) evaluate term coefficient Title: Jun 256:03 PM (3 of 8) Evaluating an algebraic expression Evaluate 3x 2y + xy for x = 2 and y = 1 3x 2y + xy Substitute 2 in for x and 1 in for y 3(2) 2(1) + (2)(1) 6 (2) + (2) Multiply first 6 + 2 + (2) To subtract, add the opposite 8 + (2) Add from left to right 6 Add Title: Jun 256:03 PM (4 of 8) Properties for Simplifying Algebraic Expressions Let a, b, and c represent real numbers Definition of Subtraction a b = a + (b) Definition of Division _a 1_ _ a b = = a , b = 0 b b Distributive Property for Subtraction a(b c) = ab ac .. . Multiplication by 1 . . 1 a = 1 Opposite of a Sum (a + b) = a + (b) Opposite of a Difference (a b) = b a Opposite of a Product (ab) = a b = a (b) Opposite of an Opposite (a) = a Multiplication by 0 Title: Jun 256:03 PM (5 of 8) 0 a = 0 . . Simplifying Algebraic Expressions Simplify by combining like terms 2(a + b) + 5a 3b 2a 2b + 5a 3b Distributive property 2a + 5a 2b 3b Commutative property of addition 2a + 5a (2b + 3b) Opposite of a sum (2 + 5)a (2 + 3)b Distributive property 3a 5b Addition Title: Jun 256:03 PM (6 of 8) Finding Perimeter Find the perimeter of each figure. Simplify the answer. 4x 2y y y 2x + y 2x 4x y Title: Jun 256:03 PM (7 of 8) homework page: 15 17 #'s: 4 84, multipls of 4 Title: Jun 256:03 PM (8 of 8)