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Chapter 2 Equations, Inequalities, and Problem Solving § 2.1 Simplifying Algebraic Expressions Terms A term is a number, or the product of a number and variables raised to powers – (the number is called a coefficient). Examples of Terms 7 (coefficient is 7) 5x3 (coefficient is 5) 4xy2 (coefficient is 4) z2 (coefficient is 1) Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Like Terms Like terms contain the same variables raised to the same powers. You can combine like terms by adding or subtracting them (this is not true for unlike terms). To combine like terms, add or subtract the numerical coefficients (as appropriate), then multiply the result by the common variable factors. Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Combining Like Terms Examples of Combining Terms Terms Before Combining After Combining Terms 6x2 + 7x2 13x2 19xy – 30xy – 11xy 13xy2 – 7x2y Can’t be combined (since the terms are not like terms) Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Using the Distributive Property Example: Find each product by using the distributive property to remove the parentheses. a.) 2(x + y) b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c) a.) 2(x + y) = 2x + 2y b.) 7(x + 2y – 5z) = 7x + 14y – 35z c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 Word Phrases as Algebraic Expressions Addition (+) sum plus added to more than increased by total Subtraction (–) difference minus subtract less than decreased by less Multiplication (·) product times multiply multiplied by of double/triple Martin-Gay, Beginning and Intermediate Algebra, 4ed Division () quotient divide shared equally among divided by divided into 7 Word Phrases as Algebraic Expressions Example: Write as an algebraic expression. Use x to represent “a number.” a.) 5 decreased by a number b.) The quotient of a number and 12 a.) In words: 5 decreased by a number – Translate: 5 x The quotient of b.) In words: a number Translate: x and 12 12 or x 12 Martin-Gay, Beginning and Intermediate Algebra, 4ed 8