114 Chapter 1 The Set of Real Numbers Properties of Real Numbers and Simplifying Expressions Section 1.6 Key Concepts Properties of Real Numbers Commutative Properties a b b a ab ba Associative Properties 1a b2 c a 1b c2 1ab2c a1bc2 Identity Properties 0 a a 1 a a Inverse Properties a 1a2 0 for b 0 1 b 1 b Distributive Property of Multiplication over Addition a1b c2 ab ac A term is a constant or the product or quotient of constants and variables. The coefficient of a term is the numerical factor of the term. Like terms have the same variables, and the corresponding variables have the same powers. Terms can be added or subtracted if they are like terms. Sometimes it is necessary to clear parentheses before adding or subtracting like terms. Examples Example 1 152 172 172 152 3 8 8 3 Example 2 12 32 10 2 13 102 12 42 5 2 14 52 Example 3 0 152 5 1182 8 Example 4 1.5 11.52 0 6 1 6 1 Example 5 21x 3y2 122x 12213y2 Example 6 2x 6y is a term with coefficient . is a term with coefficient 1. 2x 2 5x yz2 3x and are like terms. and 4ab are not like terms. 4a2b Example 7 2w 41w 22 3 2w 4w 8 3 6w 11 Clear parentheses. Combine like terms.
miller_introductory_algebra_3e_ch1_3
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