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12–2Simplifying Algebraic ExpressionsMAIN IDEA• Use the Commutativeand AssociativeProperties to simplifyexpressions.BUILD YOUR VOCABULARY (page 292)Equivalent expressions have thevalue.The Commutative Property states that thein which numbers are added or multiplied does not changethe or .KEY CONCEPTCommutative Propertya + b = b + aa b = b aAssociative Property(a + b) + c = a + (b + c)(a b) c = a (b c)The Associative Property states that the way in whichnumbers arewhen they are addedor multiplied does not change theor.EXAMPLES Use Properties to Simplify ExpressionsSimplify the expression 4 + (6 + x).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4 + (6 + x) = ( + ) + Associative Property= + Add 4 and 6.Simplify the expression (12 + x) = 15.(12 + x) + 15 = ( + ) + Commutative Property= x + ( + ) Associative Property= x + Add 12 and 15.Simplify the expression 3(5x).3(5x) = 3 (5 x)Parentheses indicate multiplication.= ( ) Associative Property= Multiply 3 and 5.Math Connects, Course 1 295