Summary 169 Chapter 3 Summary Simplifying Expressions and Combining Like Terms Example 3 1. 5 182 8 5 2. 132 1 92 192 132 3. 17 52 11 7 15 112 4. 13 102 2 3 110 22 5. 314x 122 314x2 132 1122 12x 36 Example 4 3x 15x 7x 13 15 72x Example 5 Simplify: 31k 42 16k 102 14 Clear parentheses. 31k 42 16k 102 14 3k 12 6k 10 14 3k 6k 12 10 14 3k 8 11x Section 3.1 Properties 1. Commutative property of addition: a b b a 2. Commutative property of multiplication: a b b a 3. Associative property of addition: 1a b2 c a 1b c2 4. Associative property of multiplication: 1a b2 c a 1b c2 5. Distributive property of multiplication over addition: a1b c2 a b a c Like terms can be combined by applying the distributive property. To simplify an expression, first clear parentheses using the distributive property. Group like terms together. Then combine like terms. Examples Example 1 In the expression 12x 3, 12x is a variable term. 12 is the coefficient of the term 12x. The term 3 is a constant term. Example 2 5h and 2h are like terms because the variable factor, h, is the same. 6t and 6v are not like terms because the variable factors, t and v, are not the same. Key Concepts An algebraic expression is the sum of one or more terms. A term is a constant or the product of a constant and one or more variables. If a term contains a variable it is called a variable term. A number multiplied by the variable is called a coefficient. A term with no variable is called a constant term. Terms that have exactly the same variable factors with the same exponents are called like terms.
miller_prealgebra_2e_ch1_3
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